Conditional probability

The conditional probability of an event is the probability of the event given that another event has already occurred. For events $A$ and $B$, we write the conditional probability of $A$ given $B$ as $\mathrm{Pr}(A \mid B)$, and a formula for this conditional probability is given by the following:

$\mathrm{Pr}(A \mid B) = \mathrm{Pr}(A\textrm{ and }B) / \mathrm{Pr}(B)$.

where $\mathrm{Pr}(A\textrm{ and } B)$ is the probability of both $A$ and $B$ occurring.