1. Suppose you flip a coin twice and observe the result. Which set below describes the sample space of this experiment? I.e., which set describes every possible outcome?
Define:
-
$\lbrace H, T \rbrace$ -
$\lbrace ( H, T ), ( T, H ) \rbrace$ -
$\lbrace ( H, H ), ( T, T ) \rbrace$ -
$\lbrace ( H, T ), ( H, H ), ( T, H ), ( T, T ) \rbrace$
2. Let's keep the same experiment: flipping a coin twice. What is the probability of obtaining one head and one tail in this experiment (the order doesn't matter)?
- (A)
- (B)
- (C)
3. Consider the following experiment:
You throw a dice
Hint: Use the complement rule!
- (A)
- (B)
- (C)
- (D)
4. If you throw a dice twice and sum the result, what is the probability of getting a
- (A)
- (B)
- (C)
- (D)
5. Consider the following problem:
In an experiment there are 100 ill persons. 50 of them have headache and 50 of them have fever.
The researchers want to find the probability of a random selected person in this experiment having headache or fever. One researcher provides the following argument:
"Since 50 out of 100 have headache, the probability of having headache is 1/2. The same reasoning can be applied to having fever. Therefore, the probability that a random selected person has either fever or headache is 1."
About their argument, choose the correct option.
- It is incorrect, because it assumes that the events of having headache and fever are disjoint. This cannot be inferred by the experiment as it is stated.
- It is correct, because in this case it is an application of the sum of probabilities.
- It is incorrect, because instead of summing up the probabilities, the researcher should have multiplied it.
- It is correct, because the sum of persons with headache and with fever is exactly 100.