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Theprosecutor's fallacy is misunderstanding or confusion of twodifferent conditional probabilities: (1) the probability that adefendant is innocent, given that forensic evidence shows a match;(2) the probability that forensics shows a match, given that aperson is innocent. The prosecutor's fallacy has led to wrongconvictions and imprisonment of some innocent people. Lucia de Berkis a nurse who was convicted of murder and sentenced to prison inthe Netherlands. Hospital administrators observed suspicious deathsthat occurred in hospital wards where de Berk had been present. Anexpert testified that there was only one chance in 342 million thather presence was a coincidence. However, mathematician Richard Gillcalculated the probability to be closer to 1/50, or possibly as lowas 1/5. The court used the probability that the suspicious deathscould have occurred with de Berk present, given that she wasinnocent. The court should have considered the probability that deBerk is innocent, given that the suspicious deaths occurred whenshe was present. This error of the prosecutor's fallacy is subtleand can be very difficult to understand and recognize, yet it canlead to the imprisonment of innocent people.

What are your thoughts on this? Does the distinction betweenthe two conditional probabilities make sense? Do you have questionsfor the expert or mathematician?