Probability and the law

A Dutch nurse, who was convicted of murder in 2003 following a string of suspicious deaths at the hospitals where she worked, has been set free.  It turns out that the jury who convicted her fell prey to something called “the prosecutor’s fallacy”, an error in the application of probability theory.  Andrew Gelman blogged about it a while back, and here’s his explanation:

The big number reported to the court was an estimate (possibly greatly inflated) of the chance that so many suspicious events could have occured with Lucia present if she was in fact innocent. Mathematically speaking, however, this just isn’t at all the same as the chance that Lucia is innocent, given the evidence, which is what the court really wants to know.

To see why, suppose that police pick up a suspect and match his or her DNA to evidence collected at a crime scene. Suppose that the likelihood of a match, purely by chance, is only 1 in 10,000. Is this also the chance that they are innocent? It’s easy to make this leap, but you shouldn’t.

Here’s why. Suppose the city in which the person lives has 500,000 adult inhabitants. Given the 1 in 10,000 likelihood of a random DNA match, you’d expect that about 50 people in the city would have DNA that also matches the sample. So the suspect is only 1 of 50 people who could have been at the crime scene. Based on the DNA evidence only, the person is almost certainly innocent, not certainly guilty.

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