# Binomial distribution

the binomial distribution can be defined as the number of successes in a sequence of $n$ independent experiments, each of them leading to success with probability $p$. It is a discrete probability distribution defined on the range $[0, \infty]$.

The probability of each natural number $k$ is:

$p(k) = C_{n}^{k} p^k(1-p)^{n-k}$

where $C_{n}^{k} = \frac{n!}{k!(n-k)!}$

Bar charts of the Binomial distribution with 10000 samples for various values of the parameters