Bayes' rule expresses the conditional probability of the event A given the event B in terms of the conditional probability of the event B given the event A and the unconditional probability of A:

P(A|B) = P(B|A) ×P(A)/( P(B|A)×P(A) + P(B|A^c) ×P(A^c) ).

In this expression, the unconditional probability of A is also called the prior probability of A, because it is the probability assigned to A prior to observing any data. Similarly, in this context, P(A|B) is called the posterior probability of A given B, because it is the probability of A updated to reflect (i.e., to condition on) the fact that B was observed to occur.