SOLUTION: In manufacturing a product, 85% of the products that are produced are not defective. Of the products inspected, 10% of the good ones are seen as defective and not shipped, whereas
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Question 921918: In manufacturing a product, 85% of the products that are produced are not defective. Of the products inspected, 10% of the good ones are seen as defective and not shipped, whereas only 5% of the defective products are approved and shipped. If a product is shipped, what is the probability that it is defective? Answer by tempx(1) (Show Source):
You can put this solution on YOUR website! Defective = D
Shipped = S
Givens:
P(!D) = .85
P(D) = .15
P(!S|!D) = .1
P(S|!D) = .9
P(S|D) = .05
P(!S|D) = .95
We use Bayes' theorem to solve:
P(D|S)=(P(S|D)P(D))/(P(S|D)P(D)+P(S|!D)*P(!D)) = .0097
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