Abstract

The Prosecutor's Fallacy is a well-known hazard in the assessment of probabilistic evidence that can lead to faulty inferences. It is perhaps best known via its role in the assessment of DNA match evidence in courts of law. A prosecutor, call him Burger, presents DNA evidence in court that links a defendant, Crumb, to a crime. The conditional probability of a DNA match given that Crumb is not guilty, or p(M | ~G), is very low: according to Burger, one chance in tens of millions. Burger goes on to argue that this very low probability entails another low probability. He asserts that it is very improbable that Crumb is not guilty given the match, and so p(~G | M) is also very low. As this latter probability is precisely what the jury is called upon to assess, Burger's assertion is likely to lead the jury into convicting Crumb.