Math & Logic · Ages 18+
Riddle #214
A disease affects 1 person in 10,000. A screening test catches 99% of the people who have it, and wrongly flags 1% of the people who don't. You test positive, with no symptoms and no risk factors. Roughly what is the chance you actually have it?
You solved this one before
Answer: About 1%
Picture 10,000 people: about 1 has the disease and tests positive, while about 100 healthy people also test positive. That is roughly 1 true positive per 101 positives. Ignoring how rare the disease is — the "base rate" — is the classic error here.