For a binomial random variable,
$$ X \sim \operatorname{Binomial}(n,p) $$the probability of observing exactly $k$ successes is
$$ P(X=k) = {n \choose k} p^k(1-p)^{n-k}. $$Use the sliders below to explore how the number of trials $n$ and probability of success $p$ affect the distribution.