Bayes' Theorem

A medical test is 99% accurate. You test positive. How likely are you to actually have the disease? 99%, right? Wrong — it can be as low as 1%. The trap is the base rate: if the disease is rare, most positive tests come from the healthy majority's false positives, not the sick minority's true positives. This single error — confusing P(positive | disease) with P(disease | positive) — has wrongly terrified millions of patients. The fix is Bayes' theorem.