SOLUTION: A production process produces an item. On average, 15% of all items produced are defective. Each item is inspected before being shipped, and the inspector misclassifies an item 10%

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Question 265891: A production process produces an item. On average, 15% of all items produced are defective. Each item is inspected before being shipped, and the inspector misclassifies an item 10% of the time. What proportion of the items will be "classified as good?" What is the probability that an item is defective given that it was classified as good?
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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A production process produces an item. On average, 15% of all items produced are defective. Each item is inspected before being shipped, and the inspector misclassifies an item 10% of the time.
What proportion of the items will be "classified as good?"
P(classed as good) = 90% of Good + 10% of Bad = 0.9*0.85+0.1(0.15)= 0.78
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What is the probability that an item is defective given that it was classified as good?
P(defect | classgood) = p(defect AND classgood)/P(classgood)
= (0.1*0.15)/0.85 = 0.0176
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Cheers,
Stan H.