DNA profiling (5)

A crime has been committed. DNA has been found at the scene and it is accepted that it belongs to the perpetrator. A man whose profile matches this DNA has been arrested and put on trial. You are a member of the jury. The prosecutor calls an expert who tells you that the probability that a person, chosen from the general public at random, would fit this profile is 1 in a billion. The prosecutor asks you to accept that this is such a minute chance that it makes it virtually inevitable that the accused man is guilty. What should you make of this? Well, let's suppose that the population of the world is 7 billion (it nearly is), or to make it simpler, let's make it 7 billion and 1. Somewhere in the world is the person who committed this crime. The other 7 billion are innocent (of this crime at least). The prosecution's case is that the probability of finding this profile from an innocent person (i.e. one of the 7 billion) is 1 in a billion. In other words, using D for the DNA profile, and I for an innocent person, they have given you P(D│I) - the probability that you would get this profile, given that the person is innocent. But what you as jurors should be concerned with is P(I│D) - in other words what is the probability that a person is innocent, given that they have produced this profile? Now even if the odds really are 1 in a billion (highly debatable as we have seen) that means that there are probably something like 7 people somewhere in the world who would fit this profile, which means that the man in the dock is one of around 7 people - 6 of whom are innocent, and that make P(I│D) something like 85%! Next time we'll try and draw all these threads together.