Peter recounts the SIDS case ( = "cot death" in British), where lawyer Sally Clark was accused of murdering two of her children. In court, a pediatrician stated that the chance of both of them dying of SIDS in a family like hers was 1/73 million. The two deaths are, of course, likely not independent as they shared both environmental and genetic factors, and bad statistics were used to arrive at the figure. Sally was convicted.
Sally's sentence was eventually reversed on her second appeal, but she died in 2007. The Guardian stated "Her family said she had not recovered from the miscarriage of justice." The pediatrician, Sir Roy Meadow, faced a disrepute charge by Britain's General Medical Council, and was struck from the medical register. He was recently re-instated on appeal (stating he had not set himself up as a statistical expert).
I think this is a nice illustration of why sensitivity and specificity matter more than just something to memorize for medical boards.