The conditional probability of given that has occurred, denoted , equals
|
(1) |
which can be proven directly using a Venn Diagram. Multiplying through, this becomes
|
(2) |
which can be generalized to
|
(3) |
Rearranging (1) gives
|
(4) |
Solving (4) for
and plugging in to (1) gives
|
(5) |
See also Bayes' Formula
© 1996-9 Eric W. Weisstein
1999-05-26