---
tag: 0PHC9FE2V5
kind: concept
name: Bernoulli trial
aliases: [binomial-trial]
msc: [60A05]
uses: [0HM05N3FJD]
sources:
  - url: https://en.wikipedia.org/wiki/Bernoulli_trial
    locator: lead section
same_as:
  wikidata: Q1077800
  wikipedia: Bernoulli trial
---

## Summary

A Bernoulli trial is a [[random experiment|0HM05N3FJD]] 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|0VRWZDWW6B]].

## Remarks

The outcome of one trial, coded as $1$ for success and $0$ for failure, has the [[Bernoulli distribution|0J97P5KZY0]].
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.