(Solution) - An inspector working for a manufacturing company -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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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 its line produces 0.9% of nonconforming items.
(a) What is the probability that an item selected for inspection is classified as defective?
(b) If an item selected at random is classified as nondefective, what is the probability that it is indeed good?