Prosecutor's fallacy

Name of fallacy Prosecutor's fallacy
Type Inductive Argument, Informal Argument
Description A low probability of false matches does not mean a low probability of some false match being found
Treatment This is a statistical error. Dealt with by showing an example or the error. Consider the case: you win the lottery jackpot. You are then charged with having cheated, for instance with having bribed lottery officials. At the trial, the prosecutor points out that winning the lottery without cheating is extremely unlikely, and that therefore your being innocent must be comparably unlikely. This reasoning is intuitively faulty — it could be applied to any lottery winner, even though we know somebody wins the lottery nearly every week. The flaw in the logic is that the prosecutor has failed to take account of the low prior probability that you and not somebody else would win the lottery in the first place.