Conditional probability

Conditional probability updates the chance of an event once you know another event has happened. It is written $P(A \mid B) = \frac{P(A \text{ and } B)}{P(B)}$ (the probability of $A$ given $B$), the probability of both divided by the probability of the given event. For example, if 40 percent of students take both Spanish and art and 50 percent take Spanish, then the chance of art given Spanish is $0.40 / 0.50 = 0.8$. Restricting attention to $B$ is what given means.