Mathematics might seem a logical fit for the courts, then. Judges and juries, though, all too often rely on gut feeling. A startling example was the rape trial in 1996 of a British man, Dennis John Adams. Adams hadn’t been identified in a line-up and his girlfriend had provided an alibi. But his DNA was a 1 in 200 million match to semen from the crime scene – evidence seemingly so damning that any jury would be likely to convict him.

But what did that figure actually mean? Not, as courts and the press often assume, that there was only a 1 in 200 million chance that the semen belonged to someone other than Adams, making his innocence implausible.

It actually means there is a 1 in 200 million chance that the DNA of any random member of the public will match that found at the crime scene (see “The prosecutor’s fallacy”). The difference is subtle, but significant. In a population, say, of 10,000 men who could have committed the crime, there would be a 10,000 in 200 million, or 1 in 20,000, chance that someone else is a match too. That still doesn’t look good for Adams, but it’s not nearly as damning.

Read the whole thing, including the part about O.J. Simpson.