Table of contents

1. Bayes theorem
   1. Definition

Bayes theorem

Definition

For two events A and B, the conditional probabilities P(A|B) and P(B|A) are related by Bayes’ theorem:

\[\begin{equation} P(A|B) = \frac{P(B|A) P(A)}{P(B)} \end{equation}\]

where the probability P(B) may be obtained using the formula

\[\begin{equation} P(B) = P(B|A) P(A) + P(B|\textit{not }A) P(\textit{not }A) \end{equation}\]