Bayesian baffler

by Norman Fenton and Paul Curzon, Queen Mary University of London

Here is a counter-intuitive result that most people get wrong. It is the kind of thing that programs we write to do decision-making or to help people (here lawyers and juries) make wise decisions, need to get right. What do you estimate the probabilities are?

A criminal has left their DNA at a crime scene. Only one in every 10 million people have the DNA profile found. A suspect, Fred Smith, whose DNA matches, is put on trial. There is no other evidence. The population is 10 million people. The prosecutor claims that the probability that an innocent person has the matching DNA is one in 10 million: so Fred is guilty. The defence say the correct probability is closer to one in two. Who is correct? Is Fred’s guilt “beyond reasonable doubt”?

Here is the answer and explanation.