'A 1-in-a-million DNA match' sounds damning — until you ask how many people were tested
A forensic expert testifies that a defendant's DNA matches a crime-scene sample, and the odds of a random match are one in a million. It's tempting to conclude there's only a one-in-a-million chance the defendant is innocent. But if the database searched held ten million people, you'd expect roughly ten innocent matches by chance alone. What error is being made in jumping from 'rare match' straight to 'almost certainly guilty'?
Reveal the answer
It's the prosecutor's fallacy: confusing the probability of the evidence given innocence with the probability of innocence given the evidence, two very different numbers that are only equal by coincidence. The term was coined by legal scholars William C. Thompson and Edward Schumann in a 1987 paper analysing exactly this kind of courtroom statistical error, which has contributed to real wrongful convictions.