Discussion
A test is 99 per cent accurate for a disease affecting 1 in 10000. What is the chance a positive result is correct?
Answer: B
Among ten thousand people one has the disease and tests positive, while about a hundred of the healthy test positive falsely:
\[ \tfrac{1}{1 + 100} \approx 0.01 \]
so the posterior is about 1 per cent. Ignoring the rarity of the disease and reporting the test's accuracy instead is the base rate fallacy, and it is committed constantly in medicine and in law.
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