Conditional probability

In probability theory, conditional probability is the probability of an event occurring, given that another event has occurred. Usually this is written as $P(A\mid B)$. This is read as "probability of A given B". The two events need not be related. They also need not occur at the same time. In the most general case,

$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$

Expressed in words: The conditional probability of A occurring given B is the probability of both events occurring, divided by the probability of B occurring. As a division by zero is not defined, the probability of B occurring must not be zero.