In British trials, there is a presumption of innocence - it is for prosecutions to prove "beyond reasonable doubt" that defendants are guilty, not for defendants to prove their innocence. So all we need to do is to make reasonable estimates and show that these lead to reasonable doubt.
A similar scenario involved a couple whose baby died aged 11 weeks, everyone was sympathetic and the death was registered as �natural causes�. There was evidence of a respiratory infection, and no sign of any failure of care. A couple of years later, their second child died aged 8 weeks. This time, there was no sympathy from the professionals. Four weeks after the death the couple were arrested, and eventually the mother was charged with murdering both children. She was tried and convicted and is serving a life sentence.
From this, we must presume that the mother was proven guilty beyond reasonable doubt, in order for the jury to find her guilty. Although forensic evidence was slim and the real reason for death was disputed amongst professionals. Simply put, she was convicted because the prosecution argued, and the jury accepted, that lightning does not strike twice. A leading paediatrician speaking as an expert witness for the prosecution stated that �the chance of two children in the same family both dying a cot death was 1 in 73 million. This would mean that such a double death would occur less often than once a century in England'. Thereby condemning the woman on the basis of statistical probability as a muderer. Unfortunately this statistic has been proved wrong and perhaps had the courts presented a probability based on Bayes� theorem, this would have proven she was not-guilty. Whether she is or isn�t guilty is not for me to judge, but the use of probability is frightening since as we know statistics can be manipulated any which way we choose in order to meet our outcome requirements.