Why Intuition Fails

Most people badly overestimate the chance of having a disease after a positive test. This is the base rate fallacy: ignoring how rare the condition is. Picture 10,000 people tested for a disease that affects 1 in 1,000. About 10 of them are truly sick, and the test catches them. But a 99% accurate test also wrongly flags about 100 healthy people.

So out of roughly 110 positive results, only about 10 are real. A positive result means about a 1 in 11 chance of actually being sick, not 99 percent. This counterintuitive math has huge consequences for medical screening, criminal justice, and any field that tests for rare events.