1. The problem statement, all variables and given/known data From Mathematical Statistics and Data Analysis 3ed, Rice 1.8 #61 Suppose chips are tested and the probability they are detected if defective is 0.95, and the probability they are declared sound if they are sound is 0.97. If 0.005 of the chips are faulty. What is the probability that a chip that is declared faulty is sound? 2. Relevant equations P(A|B) = P(A[itex]\cap[/itex]B) / P(B) P(A) = [itex]\Sigma[/itex]P(A|Bi)P(Bi) 3. The attempt at a solution Let D- be the event a fault is detected Let D+ be the event no fault is detected Let Df be the event a chip is faulty Let S be the event a chip is sound P(D-|Df) = 0.95 P(D+|S) = 0.97 P(Df) = 0.005 P(S) = 1 - P(Df) = 0.995 Find P(S|D-) (the answer given is 0.86) P(S|D-) = P(D-[itex]\cap[/itex]S) / P(D-) = P(D-|S)P(S) / P(D-) So here's where I've been stuck. First I'd like to know if I've translated the problem correctly. Secondly how do I find P(D-|S) and P(D-) or am I going about this the wrong way?