Probability of Flipping Coins

Flipping Coins.py is a collection of functions that deal with coin flipping, or coin tossing, which is the practice of throwing a coin in the air and checking which side is showing when it lands. An ideal unbiased coin has a 0.5 chance for showing a head and the remaining other 0.5 chance for showing a tail with each coin flip. In contrast, biased coins tend to favor one side over the other. A biased coin, for example, might have a 0.8 probability of landing on its head, or its tail.

Installation

Simply, copy the codes and paste them to your workplace. 

Documentation

Right now, Flipping Coins.py contains the following four functions:

allPossibilities(N)

This function takes a single parameter N and returns all the possible patterns that might result from throwing coins N times.

Example 1: writing all the possible patterns in tossing one coins

 In: allPossibilities(1)
 Out: ['H', 'T']

Example 2: writing all the possible patterns in tossing three coins

 In: allPossibilities(3)
 Out: ['HHH', 'HHT', 'HTH', 'HTT', 'THH', 'THT', 'TTH', 'TTT']

probabilityXcoinsYheads(x,y,headChance=0.5)

This function takes two main parameters x and y and returns the probability of getting y heads on throwing x coins.

Example 1: calculating the probability of one head showing after flipping 2 fair coins

 In: probabilityXcoinsYheads(2,1,headChance=0.5)[3]
 Out: 0.5 

Explanation: ['HT,'TH'] out of ['HH','HT','TH','TT] so 2 out 4 which is 0.5

Example 2: calculating the probability of one head showing after flipping 2 unfair coins with the head chance of 1

 In: probabilityXcoinsYheads(2,1,headChance=1)[3]
 Out: 0

Explanation: there is a 0 chance of getting 'HT' or 'TH' because the chance of getting a head is 1

probability(sequence,coinPickChance,headChance)

Example: calcuating the chance of getting 'HH' on flibbing a coin twice from a set of 2 coins each with a differet picking chance and head chance

  In: probability("HH",[0.75,0.25],[0.5,1])
  Out: 0.4375

Explanation: the chance of picking the first coin is 0.75 with 0.25 chance of getting 'HH'. For the second coin, the picking chance is 0.25 with 1 chance of getting 'HH' (result = 0.75x0.25 + 0.25x1 = 0.4375)

simulatingFlippingCoins(success=[1], size=1, coins=[1,0], probability=[0.5,0.5], tests=1000000)

Example 1: simulating 1 million tests of two fair coin flips and obtaining the proportion of tests that produced 2 heads

  In: simulatingFlippingCoins([2],2)
  Out: 0.250262
  Comparison probabilityXcoinsYheads(2,2)[3]
  Output of Comparsion (real probability): 0.25

Example 2: simulating 1 million tests of five fair coin flips and obtaining the proportion of tests that produced 1 head

  In: simulatingFlippingCoins([1],5)
  Out: 0.156261
  Comparison: probability("HTTTT",[1],[0.5])*5
  Output of Comparsion (real probability): 0.15625

Example 3: simulating 1 million tests of ten biased coin flips and obtaining the proportion of tests that produced 5 heads

  In: simulatingFlippingCoins(success=[5],size=5,probability=[0.8,0.2])
  Out: 0.32793
  Comparison: probabilityXcoinsYheads(5,5,0.8)[3]
  Output of Comparison (real probability): 0.32768

Example 4: simulating 1 million tests of ten biased coin flips and obtaining the proportion of tests that produced at least 3 heads

  In: simulatingFlippingCoins(success=list(range(3,11)),size=10,probability=[0.15,0.85])
  Out: 0.179899
  Comparison: sum([probabilityXcoinsYheads(10,x,0.15)[3] for x in range(3,11)])
  Output of Comparison (real probability): 0.17980351963242186

Dependencies

• NumPy

Contributing

The project is open for contribution.

License

This project is licensed under the MIT License - see the LICENSE file for details.