278.A Positive Test for a Rare Disease
★★★conditional probabilityCitadel
A disease affects 0.1% of the population. A test is correct 99% of the time, meaning it returns positive for 99% of people who have the disease and negative for 99% of those who do not. Someone tests positive. What is the probability that they actually have the disease?
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Imagine testing 100,000 people and count the two kinds of positive result. The healthy group is enormous, so even a small error rate produces many false positives.
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