Probability & Brainteasers · Interview Question
A disease has 1% prevalence. A test is 99% sensitive and 99% specific. You test positive — probability you have it?
How to answer
50%. Bayes: P(D|+) = (0.99·0.01)/(0.99·0.01 + 0.01·0.99) = 0.0099/0.0198 = 1/2. True positives (0.99% of the population) exactly equal false positives (0.99%) because the low 1% base rate is offset by the 1% false-positive rate.
Key idea: Answering 99% by conflating test accuracy (sensitivity) with the posterior, ignoring the base rate that floods you with false positives.
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