Bernoulli Trial Calculator

About this calculator

A Bernoulli trial is a single random experiment with exactly two possible outcomes — success or failure — where success happens with probability p and failure with probability 1 − p, named after the 17th-century mathematician Jacob Bernoulli. For a single trial, the mean (expected value) is simply p, the variance is p(1 − p), and the standard deviation is the square root of that variance, √(p(1 − p)).

Bernoulli trials are the basic building block of the binomial distribution: running n independent Bernoulli trials with the same success probability and counting the total number of successes is exactly what the binomial distribution models. This makes the Bernoulli trial the underlying model behind coin flips, pass/fail quality inspections, click-or-no-click A/B testing results, and any yes/no outcome that statisticians want to analyze probabilistically.

Enter a success probability p and the calculator returns the mean, variance and standard deviation of that single Bernoulli trial.