**Bayes' theorem** is a formula that yields the probability of an event or the truth of a hypothesis conditioned on the observation of evidence, given priors about the likelihood of the hypothesis, the observation, and the observation conditioned on the hypothesis.

### definition

bayes_theorem_core Bayes' theorem describes how an observation should be transformed into evidence that updates a prior:

`P(A|B) = P(B|A) P(A) / P(B)`

Where

`A`

is a hypothesis,`B`

is an observed event,`P(A|B)`

is the posterior probability of the hypothesis conditioned on the observation,`P(B|A)`

is the probability of the observation if the hypothesis were true,`P(A)`

is the prior probability of the hypothesis being true, and`P(B)`

is the prior probability of observing the event.