Encyclopedia > Conditional probability

Article Content

Conditional probability

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).

If A and B are independent events (that is, the occurrence of either one does not affect the occurrence of the other in any way), then P(A ∩ B) = P(A) · P(B), so P(A|B) = P(A).

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.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia

Search over one million articles, find something about almost anything!

Featured Article

Shinnecock Hills, New York

... there are 82.8 males. For every 100 females age 18 and over, there are 78.8 males. The median income for a household in the town is $72,500, and the median income ...