The binomial distribution is an example of a discrete probability distribution.

A random variable \(X\) can be modelled with the binomial distribution if the following conditions are met:
- there is a fixed number of trials (\(n\)),
- there are only two possible outcomes (success and failure),
- there is a fixed probability of success (\(p\)), and
- the trials are independent of each other.

The binomial distribution can be denoted by \(X∼B(n,p)\).

The probability mass function of a binomially distributed random variable is given by:

\(P(X=r) = \dbinom{n}{r}p^r(1-p)^{n-r}\)