(Note: this is the case of Sally Clark, convicted in the UK in 1999, found innocent on appeal in 2003, and tragically died in 2007 of alcohol poisoning. See Innocent, 2002.)

A mother was arrested after her second baby died a few months old, apparently of sudden infant death syndrome (SIDS), exactly as her first child had died a year earlier.

According to prosecution testimony, about 2 in 17200 babies die of SIDS. So, according to their argument, there is only a probability of (2=17200)2  1=72000000 that two such deaths would happen in the same family by chance alone. In other words, according to the prosecution, the woman was guilty beyond a reasonable doubt. The jury returned a guilty verdict, even though there was no significant evidence of guilt presented beyond this argument. Which of the following is the truth of the matter?

Why?

1. Given the facts presented, the probability that the woman is guilty is greater than 99%, so the jury decided correctly.

2. The argument presented by the prosecution is irrelevant to the mother’s guilt or innocence.

3. The prosecution argument is relevant but inconclusive.

4. The prosecution argument only establishes a probability of guilt of about 16%.
5. Given the facts presented, guilt and innocence are equally likely.