The prosecutor's fallacy
A crime is committed in a city of 6 million people. A DNA sample from the scene matches a profile that occurs in one person in a million. The police search a database and find one person whose DNA matches.
The prosecutor argues: "The chance of a match if the defendant were innocent is one in a million. So the chance the defendant is innocent is one in a million."
- What is wrong with this argument?
- With no other evidence, roughly what is the probability that the matched person is the culprit?
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How many people in a city of 6 million would you expect to match a one-in-a-million profile?
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