statistical independence

Written by

The Information Architects of Encyclopaedia Britannica

Last updated

July 14, 2026

Quick Summary

Statistical independence occurs when the probability of one event happening is not affected by another event. For independent events, the conditional probability remains the same, regardless of whether other events have occurred.1

Mathematically, two events, A and B, are independent if the probability of B occurring given that A has occurred is equal to the probability of B occurring on its own. This can be expressed as (P(B|A) = P(B)).2

This concept is fundamental in probability theory and plays a key role in various statistical concepts like the law of large numbers and the central limit theorem.2

Summary created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

2 Britannica Sources

Ask Britannica AI about this topic

Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.

probability theory
Independence
One of the most important concepts in probability theory is that of “independence.” The events A and B are said to be (stochastically) independent if P(B|A) = P(B), or equivalently if
Read More
One of the most important concepts in probability theory is that of “independence.” The events A and B are said to be (stochastically) independent if P(B|A) = P(B), or equivalently if
Read More

Abraham de Moivre
The definition of statistical independence—namely, that the probability of a compound event composed of the intersection of statistically independent events is the product of the probabilities of its components—was first stated in de Moivre’s Doctrine. Many problems in dice and other games were included, some of which appeared…
Read More
The definition of statistical independence—namely, that the probability of a compound event composed of the intersection of statistically independent events is the product of the probabilities of its components—was first stated in de Moivre’s Doctrine. Many problems in dice and other games were included, some of which appeared…
Read More