Events A and B are mutually exclusive Suppose event A occurs

Events A and B are mutually exclusive. Suppose event A occurs with probability 0.67 and event B occurs with probability 0.23. Given that A does not occur, what is the probability that B occurs?

Solution

P(A) = 0.67, P(B) = 0.23

A, B are mutuall exclusive P( A and B) = 0

P(A\') = 0.23, P(B\') = 0.67

P( A and B\') = 0.23

P( B occurs given that A does n\'t Occur) = P( A\' and B) / P(A\') = 0.23/0.67 = 0.3432