The rare-marker screening test

Question

A genetic marker is carried by 1% of people. There is a screening test with these properties: if you carry the marker, the test is positive 99% of the time; if you do not carry it, the test still comes back positive 5% of the time. You take the test and it is positive.

What is the probability that you actually carry the marker?

Accepted Answer

The trap is to focus on the test's 99% and forget how rare the marker is. Work with natural frequencies, which make base rates impossible to ignore. Imagine 10,000 randomly chosen people. - Carriers: 1% of 10,000 = 100 people. The test flags 99% of them, about 99 positives. - Non-carriers: the other 9,900 people. The test wrongly flags 5% of them, which is 495 positives. So the number of positive results is 99 + 495 = 594, and only 99 of those come from true carriers. Therefore P(	ext{carrier} \mid 	ext{positive}) = \frac{99}{594} = \frac{1}{6} \approx 16.7\%. Even after a "99% accurate" po…

The rare-marker screening test

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