In November 1999, a woman was convicted of the murder of her two children. They had originally been diagnosed as cot deaths, sudden infant death syndrome. There was no obvious medical reason for them...

In November 1999, a woman was convicted of the murder of her two children. They had originally been diagnosed as cot deaths, sudden infant death syndrome. There was no obvious medical reason for them to die. One of the pieces of evidence brought to court was that the probability that two children would both die from cot death was very small. It was stated, by a paediatrician, to be one in 73 million (Watkins 2000). This was calculated from the estimated proportion of similar children dying from cot death as about one in 8 540. 8 540 times 8 540 = 73 million. This was claimed to be so unlikely that we could not believe they were cot deaths and therefore they must have been murdered.

1.       What property of probability was used here?

2.       What assumption about cot death is being made? Do you think it is plausible?

3.       What would be the effect of this assumption on the probability of two cot deaths?

4.       If it were correct, what would the probability of one in 73 million tell us about the deaths of these two children?

5.       What probability might be more useful here?

6.       What fallacy was the paediatrician making?