Conditional probabilities & evidence in court

A Dutch guy has been found guilty of murdering a girl in Bristol - and today's papers are full of the fact that the Jury were not allowed to hear that he frequented a series of quite-violent websites. Even Linda was appalled that this had not been allowed in court.

But the reason why this isn't allowed is entirely sound and is based on the fact that people are unable to distinguish between two, very-different conditional probabilities, and tend to believe the wrong one of the two when they do see them both. Actually, the fact that he had seen such website has very little effect on whether he is guilty or not.

Suppose there are 20m adult males in the UK, one of whom is her killer and suppose that 100,000 have seen the websites in question. Then suppose that there are, out of the 20m adult males, 100 potential psychopaths who might be actually willing to kill someone and that 80 of these have seen the website (a much higher proportion than of the general population because they have actively sought out such material). Then you can obtain the following conditional probabilities.

Firstly, the probability that you are a psychopath given that you have seen the website - in this case 80 / 100,000 or 1 in 12,500, 0.0008.

Secondly, the probability that you have seen the website given that you are a psychopath - in this case, 80 / 100 or "5 to 4 on", 0.8, 10,000 times the first probability.

The second probability is not relevant since you don't know that the accused is a psychopathic killer (you only know this when he is convicted - or when he confessed). And the first probability is too small to be relevant. In each case, the website evidence is not relevent.

The website in question was featured in Bizarre Magazine a year or two back and so it is not exactly secret, and quite a few of its scenes are available on the download site that I get stuff off. The few I have seen have been rather cleverly put together I thought. The girls are interviewed before the scene and their willingness to partake is clear cut. Then they are interviewed afterwards as well and again it seems clearcut that they were quite happy with what has occured. Presumably these precautions are to ensure that it is clear that the scenes are consensual. Nontheless, the scenes are very rough it seemed to me.
Typical "before" and "after" pictures. What surprises me more than the contents of the website is that a very pretty 20 year old seems so keen to be featured on it.