Definition
The prosecutor's fallacy is the error of confusing P(evidence | innocent) — the probability of seeing the evidence if the defendant is innocent — with P(innocent | evidence) — the probability that the defendant is innocent given the evidence. These two probabilities are related by Bayes' theorem but are generally very different, and treating them as equal can dramatically overstate the apparent strength of evidence.
The fallacy gets its name from prosecutors who, presenting a small random-match probability (say, one in a million), invite the jury to infer that the probability of innocence is also one in a million. That inference is unwarranted without considering the base rate of plausible suspects.
Why it matters
How it works
The corrective uses Bayes' theorem. If 1 in 1 million unrelated innocent people would match a DNA profile, and there are 10 million people who could plausibly be the offender, then about 10 innocent matches exist. If only one guilty person exists in the pool, the probability that a randomly identified match is the guilty person is 1/11 — not 999,999/1,000,000.
The correct framing always asks: 'Given the evidence, what is the probability of guilt?' — and that requires the prior, not just the likelihood. Judges in some jurisdictions now expressly warn juries against the prosecutor's fallacy; expert witnesses are increasingly required to present likelihood ratios and posterior probabilities, not raw random-match figures.