Equations being chalked on board

Take care with your calculations

“Chance of cot deaths in brothers ‘1 in 73 million’”

Sally Clark served three years of a life sentence for the murder of her two children before her conviction was overturned in 2003. In the original case, the defence had claimed that sudden infant death syndrome (SIDS) – commonly known as cot death – was responsible for the death of both boys, who died just over a year apart. The prosecution argued that such a double cot death was exceptionally unlikely and claimed murder.

The prosecution’s assertion was based on the expert testimony of Professor Sir Roy Meadow, a researcher in paediatrics. Meadow had said that the chances of one child dying from SIDS in a non-smoking, affluent family was 1 in 8,543. When working out the probability of two cot deaths in the same family, he squared this probability – multiplying 8,543 by 8,543 – to get 1 in 73 million.

This would have been the right thing to do if the two events were independent of each other, like tosses of a coin. The chance of getting two heads in a row is 1/2 x 1/2 (1/4). However, two cot deaths in the same family are not independent events; there could be underlying genetic or environmental factors that make them more likely. The Royal Statistical Society deemed Meadow’s account a “mis-use of statistics”.

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Questions for discussion

  • Even if the chance of a double cot death in the same family really was 1 in 73 million, why would this not have meant there was only a 1 in 73 million (0.0000014 per cent) chance of the accused being innocent? Search for “prosecutor’s fallacy” online to find out more.
  • What figure should this number have been compared with to work out the relative likelihood of guilt or innocence?
  • Should statistical evidence in court only be presented by experts in statistics, rather than by experts in the field in which the statistics are being used?

About this resource

This resource was first published in ‘Number Crunching’ in June 2013.

Statistics and maths
Number Crunching
Education levels:
16–19, Undergraduate, Continuing professional development