The probability of surviving a certain operation is .55. If a patient survives the operations, the propability that his or her body will reject the transplant within a month is .20. What is the probability of surviving both these critical stages. I am going to say P(A) = .55 and P(B | A ) = .20 They want to know what is the probability that P(A and B) right? So, P(B | A) = P(A and B) / P(A) so P(A) * P(A|B) = P( A and B) . so P(A and B) = .55(.20) = .11. But the answer in the back of my book is saying .44 Can someone explain why I am not getting the right answer?