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
© 19969 Eric W. Weisstein
19990526