# Bayes' theorem

## Description

In probability theory, a conditional probability measures the probability of an event given that (by assumption, presumption, assertion or evidence) another event has occurred. If the events are A and B respectively, this is said to be “the probability of A given B”. It is commonly denoted by P(A|B), or sometimes PB(A). In case that both “A” and “B” are categorical variables, conditional probability table is typically used to represent the conditional probability. Bayes’ theorem (alternatively Bayes’ law or Bayes’ rule) relates current to prior belief. It also relates current to prior evidence. It is important in the mathematical manipulation of conditional probabilities. Bayes’s rule can be derived from more basic axioms of probability, specifically conditional probability.

Related formulas

## Variables

 P(A|B) The conditional probability ( the degree of belief in A having accounted for B) (dimensionless) P(B|A) The conditional probability ( the degree of belief in B having accounted for A) (dimensionless) P(A) The prior probability ( the initial degree of belief in A) (dimensionless) P(B) The prior probability ( the initial degree of belief in B) (dimensionless)