Prosecutor's fallacy
Also called: Transposed conditional
Mixing up “how likely is this evidence if the person is innocent?” with “how likely is it that the person is innocent, given this evidence?”
How to spot it
A tiny number such as one in a million is quoted as if it were the chance the accused, the patient or the theory is wrong. Ask how many others would also match.
Example
“Only one person in a million has this match, and the accused has it, so there is a one in a million chance he is innocent.” (In a city of ten million, about ten people match.)
How to answer it
Ask how many people would match, and how likely the suspect was before this evidence. Then count the others who fit as well.
Related
- Base rate fallacy: Judging a probability from a striking detail while ignoring how common the thing is overall.
- Conjunction fallacy: Thinking two things together are more likely than one of them alone.
- Texas sharpshooter: Finding a pattern in the data after the fact, and treating it as if it had been predicted.