Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

In 1999 a British woman was sentenced to life in prison for the murders of two of her children. However, the two deaths could have been entirely accidental; every year, just under three hundred babies in the UK die unexpectedly from sudden infant death syndrome (SIDS). During the trial, the jury had to decide if she was guilty of murder beyond reasonable doubt. Was she the perpetrator or the victim in this emotionally charged case? The jury was presented with stats that seemed to imply that two siblings both dying of SIDS was extremely rare. They returned a verdict of guilty (with a majority of ten to two), but the defendant’s conviction was later overturned. At the trial, erroneous statistics were presented, which gave the false impression that there was only a 0.0000014 percent chance (around one in 73 million) of two babies in such a family dying from SIDS. The Royal Statistical Society claimed there was “no statistical basis” for this figure and was concerned by the “misuse of statistics in the courts.” Upon a second appeal in 2003, the conviction was quashed, the woman having already spent three years in prison. How could math have gone so far wrong as to convict an innocent woman? The prosecution had taken the probability of a crib death in a family such as this woman’s at 1 in 8,543 and multiplied 1⁄8,543 by 1⁄8,543 to estimate the probability of two deaths.