A drug has approval probability 0.95 if tests show no side effects and 0.50 if tests show side effects. A physician assigns probability 0.20 that tests show side effects. Given approval, find the probability the drug causes side effects under this test-outcome model, to three decimals.
Let S denote the side-effect outcome and A approval. Total approval probability=.95×.8+.50×.2=.86. Bayes’ rule gives P(S|A)=P(A|S)P(S)/P(A)=.50×.2/.86=.116279, or .116. The source identifies the test side-effect outcome with the event being estimated.
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