Doctors and lawyers should get probability theory right

In a recent case of DNA evidence the probability of a chance match was quoted as 20 million to one. The accurate statement—that the defendant or two other unknown people in the United Kingdom could have committed the offence—is much less impressive. Other evidence was overwhelming, but this may not always be true, especially with matches from DNA databases. Even more problematic than the issue of presenting statistical evidence fairly is the problem of getting it wrong.

On 9 November at Chester Crown Court Sally Clark, a Cheshire solicitor, was convicted, by 10-2 majority, of smothering her two infant children. With conflicting forensic evidence, the Crown's case was bolstered by an eminent paediatrician testifying that the chances of two cot deaths happening in this family was vanishingly small—1 in 73 million. This seriously misunderstands probability theory. It is speculation whether Sally Clark would have been acquitted without this evidence. But with this mathematical error prominent the conviction is unsafe.

Imagine an archery target with two arrows sticking in the very centre of it. …