"The prosecutor's fallacy is such an easy mistake to make," says Ian Evett from the Forensic Science Service in England and Wales. It confuses two subtly different probabilities that Bayes's formula distinguishes: P(H|E), the probability that someone is innocent if they are a match to a piece of evidence, and P(E|H), the probability that someone is a match to a piece of evidence if they are innocent (see "Bayes on trial", previous page). The first probability is what we would like to know; the second is what forensics usually tells us.
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