Exercise 1 - Statistics in the Courtroom

In 1999 in England Sally Clark was found guilty of the murder of two of her sons. Both infants were found dead in the morning, one in 1996 and another in 1998, and she claimed the cause of death was sudden infant death syndrome (SIDS). No evidence of physical harm was found on the two infants so the main piece of evidence against her was the testimony of Professor Sir Roy Meadow, who testified that the chances of two infants dying of SIDS was 1 in 73 million. He arrived at this figure by finding that the rate of SIDS was 1 in 8,500 and then calculating that the chance of two SIDS cases was 8,500 \(\times\) 8,500 \(\approx\) 73 million.

Based on what we've learned throughout this course, which statement best describes a potential flaw in Sir Meadow's reasoning?

Possible answers

Sir Meadow assumed the second death was independent of the first son being affected, thereby ignoring possible genetic causes.

There is no flaw. The multiplicative rule always applies in this way: \(\mbox{Pr}(A \mbox{ and } B) =\mbox{Pr}(A)\mbox{Pr}(B)\)

Sir Meadow should have added the probabilities: \(\mbox{Pr}(A \mbox{ and } B) =\mbox{Pr}(A)+\mbox{Pr}(B)\)

The rate of SIDS is too low to perform these types of statistics.