Problem 103 of 7
Evaluate the medical or quality-control decision from defect rate 2%, test catches defects 90%, false positive rate 5%.
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
interpret conditional probabilities and false positives/negatives.
Hidden until you reveal it.
Use conditional probabilities, base rates, and expected costs; do not infer certainty from a test result.
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Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Identify base rate and test or inspection probabilities.
2. Compute relevant conditional or expected-cost quantities.
3. State what the evidence supports and its limits.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Treating P(positive|defect) as P(defect|positive).