## What is Binomial Distribution?

A binomial random variable measures the total number of successes from n independent Bernoulli random variables, where each has a probability of success equal to p. In other words, binomial distributions are used to model counts of independent events. A binomial distribution has two parameters:

- n, the number of independent experiments; and
- p, the probability that each experiment is successful

## Example

$ P_{x}=\sum_{x=0}^{n}\left ( \frac{n}{x} \right )p^{x}q^{n-x} $

$ P_{x} $ = binomial probability

n =number of trials

$ \frac{n}{x} $= combinations

x = number of times for a specific outcome with n trials

p = probability of success on a single trial

q = probability of failure on a single trial

## Why is it important?

Banks and other financial organisations use the Binomial Distribution to calculate the chance of borrowers defaulting and use the figure to price insurance and determine how much money to hold in reserve or how much to lend.