I tried several times to make it fit in one sentence, but short of a Dickensian abuse of semi-colons it's not really possible to fully explain in a sentence. M

I tried several times to make it fit in one sentence, but short of a Dickensian abuse of semi-colons it's not really possible to fully explain in a sentence. My best effort: If you have a very large imbalance in your population vs. your target group (e.g. everybody in NYC, vs the one person who robbed a bank, or the whole population vs. people with a rare disease), then seemingly strong evidence is much weaker than it appears. Longer example: Lets say we've matched the DNA of a bank robber to someone using a test with a 1-in-a-million false positive rate. That, on its own, means there is still over a 95% chance (23/24) that they are innocent given that with 24M people in the NYC area on a given day, we would expect 24 people to match. The prosecutors fallacy would be saying that there is instead only a 1-in-a-million chance that this person is innocent.