# Bayes' theorem

In probability theory and applications, Bayes' theorem shows the relation between a conditional probability and its reverse form. For example, the probability of a hypothesis given some observed pieces of evidence and the probability of that evidence given the hypothesis. This theorem is named after Thomas Bayes (/ˈbeɪz/ or "bays") and often called Bayes' law or Bayes' rule.

## Formula

The equation used is:

${\displaystyle P(A|B)={\frac {P(B|A)\,P(A)}{P(B)}}.}$

Where:

• P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
• P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
• P(B|A) is the conditional probability of B given A. It is also called the likelihood.
• P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Other Languages
العربية: مبرهنة بايز
aragonés: Teorema de Bayes
asturianu: Teorema de Bayes
беларуская: Тэарэма Баеса
беларуская (тарашкевіца)‎: Тэарэма Баеса
български: Теорема на Бейс
čeština: Bayesova věta
Cymraeg: Theorem Bayes
Ελληνικά: Θεώρημα Μπέυζ
فارسی: قضیه بیز
Gaeilge: Teoirim Bayes
한국어: 베이즈 정리
Bahasa Indonesia: Teorema Bayes
íslenska: Formúla Bayes
עברית: חוק בייס
lietuvių: Bajeso teorema
magyar: Bayes-tétel
Nederlands: Theorema van Bayes
Piemontèis: Fórmola ëd Bayes
português: Teorema de Bayes
српски / srpski: Бајесова теорема
Basa Sunda: Téoréma Bayes
svenska: Bayes sats
Türkçe: Bayes teoremi
українська: Теорема Баєса
Tiếng Việt: Định lý Bayes