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?
Thanks!
Answer by stanbon(75887) (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.
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