1. The problem statement, all variables and given/known data A concrete beam my fail by shear or flexure. The failure probability in shear is equal to the failure probability in flexure, and the probability of failure in shear when the beam is loaded beyond is flexure capacity (ie, it has already failed in flexure) is 80%. Find the failure probability of the beam in flexure, given that that the probability of failure of the beam is 0.2. 2. Relevant equations P(A | B) = P(A [tex]\cap[/tex] B) / P(B) (conditional probability equation) 3. The attempt at a solution So I started out by giving everything that's known: P(Failure) = 0.2 ==> P(Failure Shear [tex]\cup[/tex] Failure Flexure) = 0.2 P(Failure Shear) = P(Failure Flexure) P(Failure Shear | Failure Flexure) = 0.8 What I want to do is plug into the above equation, P(A | B) = P(A [tex]\cap[/tex] B) / P(B), since this seems to be a conditional probability problem. Plugging in: 0.8 = 0.2 / P(Failure Flexure) -> P(Failure Flexure) = 0.25 = 25% However, I don't believe this is correct because I believe the 0.2 given is P(Failure Shear [tex]\cup[/tex] Failure Flexure), not P(Failure Shear [tex]\cap[/tex] Failure Flexure). I believe this because the 0.2 means probability of failure due to shear *or* flexure, which signifies union, not shear AND flexure, which signifies intersection. Could anybody steer me in the right direction? This is probably a very elementary problem but probability has never really 'clicked' with me. Thanks!