All about Binomial distribution

Binomial Probability Distribution is a discrete probability distribution used for the events that give results in ‘Yes or No’ or ‘Success or Failure’.

It’s particularly useful in scenarios where these outcomes are mutually exclusive, and the probability of success (usually denoted as “p”) and the probability of failure (usually denoted as “q”) is constant for each trial.

This distribution helps calculate the probability of getting a specific number of successes in a fixed number of trials.

Formula for Binomial distribution

Binomial Distribution Examples

Let’s say we toss a coin twice, and getting head is a success we have to calculate the probability of success and failure then, in this case, we will calculate the probability distribution as follows:

In each trial getting a head that is a success, its probability is given as p = 1/2

n = 2 as we throw a coin twice

r = 0 for no success, r = 1 for getting head once and r = 2 for getting head twice

Probability of failure q = 1 — p = 1–1/2 = 1/2.

P(Getting 1 head) = P(X = 1) = 1/2

P(Getting 2 heads) = P(X = 2) = 1/4

P(Getting 0 heads) = P(X = 0) = 1/4