(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Probability - using Bayes Theorem

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