How to find the coin toss probability in Python

Probability is simply the chance of the occurrence of an event. For example, tossing a fair coin has only two possibilities. Either heads or tails will come on top of the coin. The chance of either heads or tails is 50% or 0.5 (on a scale of 0-1).

Note: Commonly, the probability is scaled from 0 to 1.

Probability of a coin toss

The occurrence of getting either heads or tails in a fair, unbiased coin toss is always 0.5.

• Experiment: This is the case study under consideration. For example, the coin toss is the experiment in our case.

• Sample Space: This is the total number of possible outcomes in an experiment. For example, the total possible outcomes in a coin toss experiment is 2, either heads or tails. Sample space is commonly written as $S$.

• Event: This refers to a particular case in an experiment. For example, getting heads on the face of the coin is an event. The event is commonly written as $E$.

• Probability: This is the final result of the probability. The probability is commonly written as $P$.

$S (Sample Space) = 2$

$E (Event: Getting head) = 1$

$P(E) = \frac{E}{S}$ = $\frac{1}{2} = 0.5$

Coin toss simulation

Let’s try the coin toss simulation using two methods:

1. Using the random module
2. Using binomial distribution

Method 1 (using the random module)

Code explanation

• Line 1: import random loads the random module that contains many random number generation functions.

• Line 3: A function named coinToss() is defined.

• Line 4: random.choice returns a random value from the given list ["Heads", "Tails"]. It either returns Heads or Tails randomly every time this line is executed.

• Line 6-7: A for loop is set up that calls coinToss() five times, and a random value from ["Heads", "Tails"] is returned every time.

Method 2 (using binomial distribution)

In probability theory, binomial distribution is a probability distribution that gives only two possible results, either success or failure.

It uses the following equation:

$P(N) = \binom{n}{N} p^N (1-p)^{n-N}$

Here, $n$ is the number of trials executed, $N$ is the number of successes, and $p$ is the probability.

In Python, the function used for binomial distribution is numpy.random.binomial(n,p). It comes from the numpy module’s random class. It takes two parameters. One is n which is the number of trials, and the second is p which is the probability of the event under consideration.

Code explanation

• Line 1: import numpy loads the numpy module that contains the binomial function.

• Line 3: A function named coinToss() is defined that takes the probability as a parameter.

• Lines 4-5: The function numpy.random.binomial(1,p) takes two parameters, the first is the number of trials and the second is the probability value. It then generates either 0 or 1, which is stored in a variable prob and returned.

• Line 7: The probability value is set to 0.5 which is the probability of a coin toss.

• Line 8: An array named samplespace is created to store heads and tails which can be displayed to the user.

• Lines 10-12: A loop is set up that executes five times and calls the coinToss() function and displays the result from samplespace as Heads or Tails.