"Thoughtful" might be one of the most unintentionally ironic screen names
de nos jours 
The amusing (if it wasn't so serious) thing is that not-very-Thoughtful refers to a piece of bogus statistical "reasoning" with regard to the Kercher DNA trace on the knife. Her "argument" goes along these lines: if Kercher's DNA was on the knife, then what are the odds of it being there by accident/contamination vs the odds of it being there by virtue of the knife having been involved in the murder? She then "argues" that if the odds of the latter are significantly greater than the odds of the former, then one can reasonably conclude that the knife was involved in the murder.
To see such arrant nonsense come out of the mind of a supposed decent mathematician is shocking indeed, and it really speaks to the inability some pure mathematicians have to relate to the real work and to applied problems. After all, there are three fundamental problems with her flawed thesis here: 1) how does one assign an informed probability to contamination/accident? 2) how does one assign an informed probability to the knife being involved in the murder? 3) Even if one could assign informed probabilities to both of the above, what does that actually tell us in the real world about whether the DNA was the result of contamination.accident or murder?
Put the last flaw in another way: the odds of winning the jackpot prize in the UK National Lottery are something around 15 million to one. Yet at least one person (or syndicate) wins the jackpot most weeks. Rare events happen.
The ultimate irony is that not-very-Thoughtful wrote about a similar statistical fallacy in her book: the case of Sally Clark. She was erroneously convicted of murdering two of her children, largely based on the bogus statistical calculations of a prosecution expert witness who had simply (and extremely crassly) multiplied the raw odds of sudden natural child death (cot death syndrome) by itself in order to give the odds of it happening twice to the same mother. The incidence of cot death was reckoned to be around 1 per 8,500 children in the UK, and the prosecution "expert" squared that number to give a probability of 1 in 73 million that two of Clark's children had died of cot death. He then used this bogus statistic to persuade the court that it was somehow far more likely that Clark had murdered her two children - even though he didn't have the appropriate comparator statistic of what proportion of mother kill two of their children.
And regardless of the ins-and-outs of that particular case, the odds are somewhat meaningless when trying to determine what happened. After all, consider if only one child had died. Assuming the 1-in-8,500 statistic for UK cot deaths is broadly correct, this still would make it extremely unlikely - simply on the raw stats - that the child had died of cot death syndrome. And even when we get to attempting a conditional analysis (given that a child has died, what are the odds that it died from cot death vs murder by the mother), we would need somehow to attain a reasonable comparator probability that the mother had murdered her child. And that is near-impossible, given the individual circumstances of such an event.
In summary, not-very-Thoughtful has employed flawed mathematical thinking in her confirmation-biased attempt to show how the knife must have been involved in the murder. It's a very unedifying spectacle to behold.
