In probability theory, conditional probability is the probability that some event A occurs, knowing that event B occurs.
It is written P(A|B), read "the probability of A, given B".
If A and B are events, and P(B) > 0, then
- P(A|B) = P(A ∩ B) / P(B).
events (that is, the occurrence of either one does not affect the occurrence of the other in any way), then
) = P
) · P
), so P
) = P
If B is an event and P(B) > 0, then the function Q defined by Q(A) = P(A|B) for all events A is a probability measure.
Conditional probability is more easily calculated with an decision tree.