[sterlind]

there's a particularly sad story about HIV testing, which is told as a cautionary tale to medical students: during the HIV outbreak, the tests had something like a 2% false positive rate. the result letter made the mistake of telling patients there was only a 2% chance the test was wrong. people committed suicide after discovering their test came back positive.

but they neglected conditional probability. so many people were being tested that the probability they had HIV was much lower than 98%. they changed the letters to say "inconclusive" instead of "positive" and had them take the test again, which reduced the needless suicides.