Consider a sequence of n independent Bernoulli trials with the likelihood of a success p on each individual trial stays constant from trial to trial with \(0 \lt p \lt 1 \text{.}\) If we let the variable \(X\) measure the number of successes obtained when doing a fixed number of trials n with \(R = \{ 0, 1, ..., n \}\text{,}\) then the resulting distribution of probabilities is called a Binomial Distribution.