Index: The Book of Statistical ProofsGeneral Theorems ▷ Probability theory ▷ Probability ▷ Conditional probability

Definition: (law of conditional probability, also called “product rule”) Let $A$ and $B$ be two arbitrary statements about random variables, such as statements about the presence or absence of an event or about the value of a scalar, vector or matrix. Furthermore, assume a joint probability distribution $p(A,B)$. Then, $p(A \vert B)$ is called the conditional probability that $A$ is true, given that $B$ is true, and is given by

\[\label{eq:prob-cond} p(A|B) = \frac{p(A,B)}{p(B)}\]

where $p(B)$ is the marginal probability of $B$.


Metadata: ID: D51 | shortcut: prob-cond | author: JoramSoch | date: 2020-05-10, 20:06.