The Prosecutor's Fallacy

In 1999, British solicitor Sally Clark was convicted of murdering her two infant sons. The prosecution's key evidence: a pediatrician testified that the odds of two children in one family dying of SIDS were 1 in 73 million. The jury convicted.

The math was catastrophically wrong. The expert multiplied the probability of one SIDS death (1 in 8,543) by itself, assuming independence. But SIDS deaths in the same family are not independent — genetic and environmental factors create correlation. The real probability of a second SIDS death given the first was closer to 1 in 100.

Worse, even 1-in-73-million does not mean guilt. With 700,000 births per year in the UK, such coincidences are expected.