Given:
• Accuracy: 99 %
• The disease affects: 1 in 1,000 people
A person receives a positive test result.
Question:
What is the actual probability that the person truly has the disease?
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Solution
Out of 1,000 tested people, about 1 truly has the disease and 999 do not.
With 99 % accuracy (simplified):
• The 1 sick person will very likely test positive (≈ 1 true positive).
• About 1 % of the 999 healthy people will still test positive → ≈ 10 false positives.
So you get roughly 11 positive results, but only 1 is real.
Probability of actually being sick after a positive test:
≈ 1 / 11 ≈ 9 %.
This is the base-rate fallacy: when something is rare, false positives can dominate the “positive” group.