The binomial distribution is a discrete probability distribution of the total number of 'successes' $X$ in $n$ independent trials, where each trial can result in either a 'success' or a 'failure' (e.g., heads or tails). The probability of a success in each trial is equal to $P$, and the probability of a failure is equal to $1 - P.$ The graph below shows a binomial distribution with number of trials $n$ = and a success probability per trial of $P$ = . Move the sliders to see binomial distributions with different numbers of trials and different success probabilities. If there is only one trial, $n = 1$ and the binomial distribution reduces to the bernoulli distribution.

number of trials $n$ =
success probability $P$ =