Sally Clark was convicted in 1999 of murdering two of her sons.  The two children both died suddenly as infants.   A pediatric professor testified that the odds of 2 children from the same (affluent) household dying of SIDS was 1 in 73 million.  He obtained this probability by squaring the odds of dying from SIDs for a single child (1 in 8500).  The professor got 1 in 73M by 1/(8500*8500).  Now there was  LOT wrong with this assessment, but she was convicted and stayed in prison from 1999 util January 2003 when her second re-trial ended in an acquittal.  

The forensic pathologist failed to disclose microbiological test results that indicated that the second son likely died of natural causes.

The 'odds' (actually the death rate) of 1 in 8500 was obtained by biased selection of critical factors (affluent family, non-smoking, parents got along) and the exclusion of other factors (boys succumb to SIDs more frequently than girls).  The professor also assumed (incorrectly) that the odds of 2 children from the same household dying of anything were independent.  Not so if there were a genetic component or other environmental component that resulted in their sudden death.  This is the aptly named "prosecutors fallacy", which requires that the relative odds of two competing theories be assessed.  It was actually less likely that the mother would murder both children at different times than they were to die of SIDs (or any other cause) at different times.  This fallacy also goes to the fact that 'odds' outside of the well controlled environment of gambling are not homogenously or independently distributed.  

Sally Clark eventually succumbed to alcoholism in 2007.  The courts ordered a review of similar cases and two other women were also released from prison for similar 'crimes' and similar mis-use of statistics.