DNA Cold-case: The prosecutors' fallacy just will not go away

The Daily Mail has an interesting report about the trial of John Molt who is accused of being the masked rapist who attacked a 15-year-old girl. The report says Molt was "caught after his father provided a DNA sample 12 years later".

In a previous report about the Stephen Lawrence trial I noted that the media was wrongly attributing statements to expert witnesses - reporting them as if they had made the prosecutors fallacy when in reality they did not. However, in this latest case the Daily Mail report seems to be directly quoting the prosecuting barrister:

Carolyn Gardiner, prosecuting at Chelmsford Crown Court, said: ‘The probability of that semen not coming from Jon Molt is one in a billion. Members of the jury, just think what a huge number that is.’

If that quote is accurate then it would be hard to find a more blatant example of the prosecutors' fallacy and a more ill-informed way of presenting it (and that's even if we assume that the one in a billion DNA random match probability is roughly correct, whereas it is almost certainly massively underestimated). 

The fact is that even very clever people continue to make the prosecutors' fallacy and it will continue to bias judgements. Shortly before taking on his current high-profile role no less a judicial luminary than Lord Justice Leveson told me that he still did not understand the fallacy.

Yet, at a recent meeting I attended at the Home Office (about using Bayes in court) a senior barrister asserted that 'no lawyer would EVER make the prosecutors' fallacy because it is now so widely known and understood'. This same barrister (along with others at the meeting) also ridiculed the point I had made about the Stephen Lawrence case, namely that if media reporters with considerable legal knowledge made the fallacy when interpreting what the experts had said then it is almost certain that the jury misinterpreted the evidence in the same way. In other words, although the prosecutor fallacy was not stated in court, it may still have been made in the jury's decision-making. The barrister claimed that 'no jury member sitting in court listening to the evidence would possibly make that mistake".