1. The problem statement, all variables and given/known data Basically, I'm given the probability of 4 independent events: P(A) = 0.04 P(B) = 0.03 P(C) = 0.02 P(D) = 0.01 If any one of these occur, a failure will happen. More than one can happen at the same time. I need to find the probability that more than one of them has occurred given at least one as occurred. 2. Relevant equations 3. The attempt at a solution I solved for the prob that at least one occurred: Let F = A∪B∪C∪D Then P(F) = P(A) + P(B) + P(C) + P(D) - P(A∩B∩C∩D) = 0.09999976 Now I have to solve for prob of 'more than one' occurred given F has occurred. I'm stuck on this part. How do I represent 'more than one occurred' with symbols? Would it be E = (A∩B)∪(A∩C)∪(B∩D)∪(C∩D)? Then P(E | F) ?