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bbq-probabiliy_of_progeny.txt
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bbq-probabiliy_of_progeny.txt
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MC A women has five (5) children, what is the probability that she has exactly two (2) boys and three (3) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 32 </td></tr></table></td><td> = </td><td>0.3125</td><td><strong> = </strong></td><td><strong>31.2%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>3</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10×27 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1024 </td></tr></table></td><td> = </td><td>0.2637</td><td><strong> = </strong></td><td><strong>26.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1024 </td></tr></table></td><td> = </td><td>0.0879</td><td><strong> = </strong></td><td><strong>8.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>3</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (3–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 32 </td></tr></table></td><td> = </td><td>0.0938</td><td><strong> = </strong></td><td><strong>9.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>3</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (3–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 32 </td></tr></table></td><td> = </td><td>0.0312</td><td><strong> = </strong></td><td><strong>3.1%</strong></td></tr></table> Incorrect
MC A women has five (5) children, what is the probability that she has exactly three (3) boys and two (2) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>3</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (3–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 32 </td></tr></table></td><td> = </td><td>0.0938</td><td><strong> = </strong></td><td><strong>9.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>3</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1024 </td></tr></table></td><td> = </td><td>0.0879</td><td><strong> = </strong></td><td><strong>8.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>3</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>3</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10×27 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1024 </td></tr></table></td><td> = </td><td>0.2637</td><td><strong> = </strong></td><td><strong>26.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>3</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (3–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 32 </td></tr></table></td><td> = </td><td>0.0312</td><td><strong> = </strong></td><td><strong>3.1%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 32 </td></tr></table></td><td> = </td><td>0.3125</td><td><strong> = </strong></td><td><strong>31.2%</strong></td></tr></table> Correct
MC A women has six (6) children, what is the probability that she has exactly two (2) boys and four (4) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 15 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 64 </td></tr></table></td><td> = </td><td>0.2344</td><td><strong> = </strong></td><td><strong>23.4%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>4</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 15×81 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4096 </td></tr></table></td><td> = </td><td>0.2966</td><td><strong> = </strong></td><td><strong>29.7%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 15×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4096 </td></tr></table></td><td> = </td><td>0.0330</td><td><strong> = </strong></td><td><strong>3.3%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>4</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (4–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 64 </td></tr></table></td><td> = </td><td>0.0156</td><td><strong> = </strong></td><td><strong>1.6%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>4</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (4–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 64 </td></tr></table></td><td> = </td><td>0.0938</td><td><strong> = </strong></td><td><strong>9.4%</strong></td></tr></table> Incorrect
MC A women has six (6) children, what is the probability that she has exactly four (4) boys and two (2) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>4</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 15×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4096 </td></tr></table></td><td> = </td><td>0.0330</td><td><strong> = </strong></td><td><strong>3.3%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>4</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>4</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 15×81 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4096 </td></tr></table></td><td> = </td><td>0.2966</td><td><strong> = </strong></td><td><strong>29.7%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>4</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (4–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 64 </td></tr></table></td><td> = </td><td>0.0156</td><td><strong> = </strong></td><td><strong>1.6%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>4</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (4–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 64 </td></tr></table></td><td> = </td><td>0.0938</td><td><strong> = </strong></td><td><strong>9.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 15 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 64 </td></tr></table></td><td> = </td><td>0.2344</td><td><strong> = </strong></td><td><strong>23.4%</strong></td></tr></table> Correct
MC A women has seven (7) children, what is the probability that she has exactly two (2) boys and five (5) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>7</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 21 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.1641</td><td><strong> = </strong></td><td><strong>16.4%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.0078</td><td><strong> = </strong></td><td><strong>0.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.0781</td><td><strong> = </strong></td><td><strong>7.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>5</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 21×243 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 16384 </td></tr></table></td><td> = </td><td>0.3115</td><td><strong> = </strong></td><td><strong>31.1%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 21×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 16384 </td></tr></table></td><td> = </td><td>0.0115</td><td><strong> = </strong></td><td><strong>1.2%</strong></td></tr></table> Incorrect
MC A women has seven (7) children, what is the probability that she has exactly three (3) boys and four (4) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>4</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (4–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.0078</td><td><strong> = </strong></td><td><strong>0.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>3</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>3</sup>4<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 35×27 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 16384 </td></tr></table></td><td> = </td><td>0.0577</td><td><strong> = </strong></td><td><strong>5.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>4</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (4–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.0312</td><td><strong> = </strong></td><td><strong>3.1%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>4</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>3</sup>4<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 35×81 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 16384 </td></tr></table></td><td> = </td><td>0.1730</td><td><strong> = </strong></td><td><strong>17.3%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>7</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 35 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.2734</td><td><strong> = </strong></td><td><strong>27.3%</strong></td></tr></table> Correct
MC A women has seven (7) children, what is the probability that she has exactly four (4) boys and three (3) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>4</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (4–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.0078</td><td><strong> = </strong></td><td><strong>0.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>7</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 35 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.2734</td><td><strong> = </strong></td><td><strong>27.3%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>4</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (4–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.0312</td><td><strong> = </strong></td><td><strong>3.1%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>4</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>4</sup>4<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 35×81 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 16384 </td></tr></table></td><td> = </td><td>0.1730</td><td><strong> = </strong></td><td><strong>17.3%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>3</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>4</sup>4<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 35×27 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 16384 </td></tr></table></td><td> = </td><td>0.0577</td><td><strong> = </strong></td><td><strong>5.8%</strong></td></tr></table> Incorrect
MC A women has seven (7) children, what is the probability that she has exactly five (5) boys and two (2) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.0078</td><td><strong> = </strong></td><td><strong>0.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>5</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 21×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 16384 </td></tr></table></td><td> = </td><td>0.0115</td><td><strong> = </strong></td><td><strong>1.2%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>7</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 21 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.1641</td><td><strong> = </strong></td><td><strong>16.4%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 128 </td></tr></table></td><td> = </td><td>0.0781</td><td><strong> = </strong></td><td><strong>7.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>5</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>5</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 21×243 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 16384 </td></tr></table></td><td> = </td><td>0.3115</td><td><strong> = </strong></td><td><strong>31.1%</strong></td></tr></table> Incorrect
MC A women has eight (8) children, what is the probability that she has exactly two (2) boys and six (6) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.0039</td><td><strong> = </strong></td><td><strong>0.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 28×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 65536 </td></tr></table></td><td> = </td><td>0.0038</td><td><strong> = </strong></td><td><strong>0.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>8</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>8</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 28 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.1094</td><td><strong> = </strong></td><td><strong>10.9%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>6</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 28×729 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 65536 </td></tr></table></td><td> = </td><td>0.3115</td><td><strong> = </strong></td><td><strong>31.1%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 15 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.0586</td><td><strong> = </strong></td><td><strong>5.9%</strong></td></tr></table> Incorrect
MC A women has eight (8) children, what is the probability that she has exactly three (3) boys and five (5) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>8</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7⋅6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>8</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 56 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.2188</td><td><strong> = </strong></td><td><strong>21.9%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.0391</td><td><strong> = </strong></td><td><strong>3.9%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7⋅6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>5</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>3</sup>4<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 56×243 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 65536 </td></tr></table></td><td> = </td><td>0.2076</td><td><strong> = </strong></td><td><strong>20.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7⋅6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>3</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>3</sup>4<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 56×27 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 65536 </td></tr></table></td><td> = </td><td>0.0231</td><td><strong> = </strong></td><td><strong>2.3%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.0039</td><td><strong> = </strong></td><td><strong>0.4%</strong></td></tr></table> Incorrect
MC A women has eight (8) children, what is the probability that she has exactly five (5) boys and three (3) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7⋅6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>3</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>5</sup>4<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 56×27 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 65536 </td></tr></table></td><td> = </td><td>0.0231</td><td><strong> = </strong></td><td><strong>2.3%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 10 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.0391</td><td><strong> = </strong></td><td><strong>3.9%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7⋅6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>5</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>5</sup>4<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 56×243 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 65536 </td></tr></table></td><td> = </td><td>0.2076</td><td><strong> = </strong></td><td><strong>20.8%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.0039</td><td><strong> = </strong></td><td><strong>0.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>8</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7⋅6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>8</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 56 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.2188</td><td><strong> = </strong></td><td><strong>21.9%</strong></td></tr></table> Correct
MC A women has eight (8) children, what is the probability that she has exactly six (6) boys and two (2) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.0039</td><td><strong> = </strong></td><td><strong>0.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>6</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>6</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 6⋅5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>6</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 28×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 65536 </td></tr></table></td><td> = </td><td>0.0038</td><td><strong> = </strong></td><td><strong>0.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>8</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 6⋅5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>8</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 28 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.1094</td><td><strong> = </strong></td><td><strong>10.9%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 15 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 256 </td></tr></table></td><td> = </td><td>0.0586</td><td><strong> = </strong></td><td><strong>5.9%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>8</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>6</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (8–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>6</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 8⋅7 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 6⋅5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>6</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>6</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 28×729 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 65536 </td></tr></table></td><td> = </td><td>0.3115</td><td><strong> = </strong></td><td><strong>31.1%</strong></td></tr></table> Incorrect
MC A women has nine (9) children, what is the probability that she has exactly two (2) boys and seven (7) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>7</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 36×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.0012</td><td><strong> = </strong></td><td><strong>0.1%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>7</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 21 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0410</td><td><strong> = </strong></td><td><strong>4.1%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>2</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>7</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>2</sup>4<sup>7</sup> </td></tr></table></td><td> = </td><td></td><td> = </td><td>0.3003</td><td><strong> = </strong></td><td><strong>30.0%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>7</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–7)! ⋅ 7! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>7</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0020</td><td><strong> = </strong></td><td><strong>0.2%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>9</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>9</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 36 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0703</td><td><strong> = </strong></td><td><strong>7.0%</strong></td></tr></table> Correct
MC A women has nine (9) children, what is the probability that she has exactly three (3) boys and six (6) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>3</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>3</sup>4<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 84×27 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.0087</td><td><strong> = </strong></td><td><strong>0.9%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>9</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>9</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 84 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.1641</td><td><strong> = </strong></td><td><strong>16.4%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 20 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0391</td><td><strong> = </strong></td><td><strong>3.9%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>3</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>6</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>3</sup>4<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 84×729 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.2336</td><td><strong> = </strong></td><td><strong>23.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0020</td><td><strong> = </strong></td><td><strong>0.2%</strong></td></tr></table> Incorrect
MC A women has nine (9) children, what is the probability that she has exactly four (4) boys and five (5) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup>⋅(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0098</td><td><strong> = </strong></td><td><strong>1.0%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup>⋅(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0020</td><td><strong> = </strong></td><td><strong>0.2%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6⋅5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>4</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>4</sup>4<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 126×81 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.0389</td><td><strong> = </strong></td><td><strong>3.9%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>4</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6⋅5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>5</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>4</sup>4<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 126×243 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.1168</td><td><strong> = </strong></td><td><strong>11.7%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup>⋅(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>9</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6⋅5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>9</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 126 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.2461</td><td><strong> = </strong></td><td><strong>24.6%</strong></td></tr></table> Correct
MC A women has nine (9) children, what is the probability that she has exactly five (5) boys and four (4) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup>⋅(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0020</td><td><strong> = </strong></td><td><strong>0.2%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>4</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>5</sup>4<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 126×81 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.0389</td><td><strong> = </strong></td><td><strong>3.9%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>5</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>5</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>5</sup>4<sup>4</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 126×243 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.1168</td><td><strong> = </strong></td><td><strong>11.7%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>5</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup>⋅(<span style='font-size: large;'>½</span>)<sup>4</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–5)! ⋅ 5! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>9</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7⋅6 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>9</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 126 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.2461</td><td><strong> = </strong></td><td><strong>24.6%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>5</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>4</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>4</sup>⋅(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (5–4)! ⋅ 4! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>5</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>5</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 5 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0098</td><td><strong> = </strong></td><td><strong>1.0%</strong></td></tr></table> Incorrect
MC A women has nine (9) children, what is the probability that she has exactly six (6) boys and three (3) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>3</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>3</sup>⋅(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–3)! ⋅ 3! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6⋅5⋅4 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 20 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0391</td><td><strong> = </strong></td><td><strong>3.9%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>6</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>6</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 6⋅5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>6</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>6</sup>4<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 84×729 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.2336</td><td><strong> = </strong></td><td><strong>23.4%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>6</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>6</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 6⋅5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>3</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>6</sup>4<sup>3</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 84×27 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.0087</td><td><strong> = </strong></td><td><strong>0.9%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>6</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 6! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (6–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>6</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0020</td><td><strong> = </strong></td><td><strong>0.2%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>6</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>6</sup>⋅(<span style='font-size: large;'>½</span>)<sup>3</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–6)! ⋅ 6! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>9</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8⋅7 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 6⋅5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>9</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 84 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.1641</td><td><strong> = </strong></td><td><strong>16.4%</strong></td></tr></table> Correct
MC A women has nine (9) children, what is the probability that she has exactly seven (7) boys and two (2) girls? <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>7</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–7)! ⋅ 7! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>9</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 7⋅6⋅5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>9</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 36 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0703</td><td><strong> = </strong></td><td><strong>7.0%</strong></td></tr></table> Correct <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>7</td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>7</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–7)! ⋅ 7! </td></tr></table></td><td>(<span style='font-size: large;'>¾</span>)<sup>7</sup>⋅(<span style='font-size: large;'>¼</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 7⋅6⋅5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>7</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>7</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td></td><td> = </td><td>0.3003</td><td><strong> = </strong></td><td><strong>30.0%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>9</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>7</td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>7</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (9–7)! ⋅ 7! </td></tr></table></td><td>(<span style='font-size: large;'>¼</span>)<sup>7</sup>⋅(<span style='font-size: large;'>¾</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 9⋅8 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 7⋅6⋅5⋅4⋅3⋅2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 3<sup>2</sup> </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 4<sup>7</sup>4<sup>2</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 36×9 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 262144 </td></tr></table></td><td> = </td><td>0.0012</td><td><strong> = </strong></td><td><strong>0.1%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>7</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup>⋅(<span style='font-size: large;'>½</span>)<sup>2</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–7)! ⋅ 7! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 1 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>7</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0020</td><td><strong> = </strong></td><td><strong>0.2%</strong></td></tr></table> Incorrect <table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>(</span></td> <td style='text-align: center; vertical-align: middle;'>7</td> <td rowspan=2 style='text-align: center; vertical-align: middle;'> <span style='font-size: x-large;'>)</span></td></tr><tr> <td style='text-align: center; vertical-align: middle;'>2</td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>2</sup>⋅(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7! </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> (7–2)! ⋅ 2! </td></tr></table></td><td>(<span style='font-size: large;'>½</span>)<sup>7</sup></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 7⋅6⋅5⋅4⋅3 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2 </td></tr></table></td><td>×</td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 1 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 2<sup>7</sup> </td></tr></table></td><td> = </td><td><table border=1 style='border-collapse: collapse; border: 1px solid white;'><tr> <td style='text-align: center; vertical-align: middle; border-bottom: 1px solid black;'> 21 </td></tr><tr> <td style='text-align: center; vertical-align: middle; border-top: 1px solid black;'> 512 </td></tr></table></td><td> = </td><td>0.0410</td><td><strong> = </strong></td><td><strong>4.1%</strong></td></tr></table> Incorrect