An inspector working for a manufacturing company has a 99% chance of correctly i

Question

An inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has evidence that of the items its line produces are nonconforming. What is the probability that an item selected for inspection is classified as defective? If an item selected at random is classified as non defective, what is the probability that it is indeed good? Let D be the event that a part is classified as defective. Let G be the event that the part is good.

Explanation / Answer

Let B1: The selected item is defective =8% =0.08

and B2: The selected item is defective=1-0.08=0.92

a) Let D: The item is classified as defective =P(D)= 0.99*0.08+0.005*0.92=0.0838

b) P(G)=1-P(D)=1-0.0838=0.9162

Probability is given by 0.005*0.92/0.9162=0.005

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