Question: A production process produces an item. On average15% of all items prod

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Question: A production process produces an item. On average15% of all items produced are defective.Each item is inspectedbefore being shippedand the inspector misclassifies an item 10% ofthe time. A- what proportion of the items will be classified asgood B-What is the probability that an item is defective given thatit was classified as good. show formula and calculation Question: A production process produces an item. On average15% of all items produced are defective.Each item is inspectedbefore being shippedand the inspector misclassifies an item 10% ofthe time. A- what proportion of the items will be classified asgood B-What is the probability that an item is defective given thatit was classified as good. show formula and calculation

Explanation / Answer

A. (0.85)(0.90) + (0.15)(0.10) = 0.78 ==> 78% B. (0.15)(0.10)/(0.78) = 0.019231 ==> 1.9% EDIT: Since 10% are filed incorrectly, there's a 90% change that agood item will be correctly filed as good and a 10% chance that abad item will be incorrectly filed as good. So in part a wehave: P(good)*P(filed good|good) + P(bad)*P(filed good|bad) In part b we have: P(bad and filed good)/P(filed good)

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