# Bayes' theorem

Definition from Wiktionary, the free dictionary

## Contents

## English[edit]

### Etymology[edit]

Named after Thomas Bayes (1701–1761), English mathematician.

### Noun[edit]

**Bayes' theorem** (*uncountable*)

- A theorem which states that an already-known unconditioned probability (the "prior") of some target event can be multiplied by a "likelihood ratio" — the conditional probability of a certain factor event (given the prior) divided by the marginal probability of that factor — in order to obtain the ("posterior", i.e., the) conditional probability of the target given the factor.

#### Usage notes[edit]

- The "marginal probability" is the unconditioned probability of the factor, which can be expanded, by means of the law of total probability, into a sum of terms. Each term is the product of the conditional probability of the factor given some event which shares the same sample space as the target, and the unconditioned probability of that event.