Bernoulli Distribution

The Bernoulli distribution is the simplest distribution of all: a single yes/no trial that succeeds with probability p and fails with probability 1 minus p. A single coin flip, one click-or-no-click, or one customer buying-or-not are all Bernoulli outcomes.

It is the atom from which richer distributions are built — stack many independent Bernoulli trials and you get a binomial. Its mean is just p and its variance is p times (1 minus p), which is largest when p is 0.5, meaning a fair 50/50 event is the most unpredictable.