A disease test is 99% accurate. You test positive. How worried should you be?
A disease affects 1 in 10,000 people. A test for it is 99% accurate: it correctly flags 99% of people who have the disease, and correctly clears 99% of people who don't. You take the test and get a positive result. What's the actual probability you have the disease?
Reveal the answer
Only about 1%. Out of 10,000 people, roughly 1 person actually has the disease and tests positive, but the test also falsely flags about 1% of the other 9,999 healthy people, close to 100 false positives. Among everyone who tests positive, true cases are vastly outnumbered by false alarms. Ignoring how rare the condition is to begin with, and focusing only on the test's accuracy, is the base rate fallacy, a well-documented error even among trained doctors estimating real diagnostic odds.
— Amos Tversky and Daniel Kahneman, Judgment under Uncertainty: Heuristics and Biases — Science, 1974