1. The problem statement, all variables and given/known data Question breaks down to this. defect occurs 1/100 items. .97 (97%) of the time when an item has a defect it is detected. .005 of the time, an item is detected to have a defect when it actually does not have one. What is the probability that an Actual defect occurs when one is detected? 2. Relevant equations I can use Bayes theorem, once I know the variables but this is where I am having trouble with this question. Determining what A1, A2 are? B = A defect being found (I believe) P(B|A1)= ? P(B|A2)=? 3. The attempt at a solution I believe I want to find P(A1|B) which will be the probability that a detection is actually a defect when found. I know P(B|A1), P(B|A2) must = 1 which is where I can not seem to figure out in this case. I think A1 = Defect being found correctly = .97 and A2 = Defect being found incorrectly = ? (.005 but is that it? or how is this calculated given this is 99/100 times .005 are found incorrectly?). Any help would be awesome! Thanks
I find it most helpful in such problems to use a suggestive notation, such as: AD = actually defective, AN = actually non-defective, DD = detected as defective and DN = detected as non-defective. You are given P{AD} = 1/100, so you can get P{AN} (how?). You are also given P{DD|AD} = 0.97, so you can get P{DN|AD} (how?). Finally, you are given P{DD|AN} = 0.005, so you can get P{DN|AN} (how?). Now you want to compute P{AD|DD}. You can use the standard formulas to get this, but I won't spoil your fun by showing you how. RGV