Bernoulli trial

Summary

A Bernoulli trial is a random experiment with exactly two possible outcomes, called success and failure. The probability $p$ of success is the same each time the trial is repeated, and the failure has probability $q = 1 - p$. A sequence of Bernoulli trials usually means independent repetitions of one trial. The number of successes in $n$ such trials has the binomial distribution.

Remarks

The outcome of one trial, coded as $1$ for success and $0$ for failure, has the Bernoulli distribution. The trials are named after Jacob Bernoulli, who studied them in his book Ars Conjectandi of 1713. Examples are a coin toss, with heads as success, and a roll of a die, with a six as success and $p = 1/6$.

Explanations

L1 human

A Bernoulli trial is a yes-or-no experiment. Many questions have this form: does the coin show heads, does the patient recover, does the part fail.