# Binomial distribution

From AMS Glossary

## binomial distribution

A probability distribution that applies to experiments involving sequences of independent trials in which only two possible outcomes (e.g., success or failure) can result on each trial.

If

*p*is the probability of success on each trial, and*q*= 1 -*p*the probability of failure, then the probability of success occurring*x*times in*n*trials is given by the binomial distribution: