Probability in Court
This resource is part of the collection Probability and Evidence.
Take a look at this video, where Prof Dawid discusses some of the ways in which probability has been used inappropriately in court cases.
Sally Clark and Sudden Infant Death Syndrome (SIDS)
- In 1996, her first son died apparently of SIDS (also known as "cot death") at a few weeks of age.
- In 1998, her second son died similarly.
- She was convicted for their murder when the expert witness for the prosecution said the chance of the two deaths happening accidentally was 1 in 73 million.
- There was virtually no other evidence
The expert used the following method to calculate the probability:
- The probability of SIDS in an affluent family where neither parent smokes and the mother is aged over 26 is approximately $\tfrac{1}{8500}$.
- The probability of this happening to both of the children is therefore $\left( \tfrac{1}{8500} \right)^2 = \tfrac{1}{72,250,000}$.
What assumption has the expert made?
When you've thought about this question, click the button below.
The expert has assumed that the events are independent: so the second death is no more or less likely to occur once you know about the first one.
Do you think that this is a reasonable assumption to make?
It might help you to know that:
- SIDS is the name given to sudden, unexpected and unexplained deaths in apparently healthy babies.
- There may be as yet undiscovered genetic causes for SIDS.
- There may be hidden environmental causes for SIDS.
Two cases of SIDS in the same family is an extremely rare event.
So too is a double murder of two babies - this probability can be estimated as 1 in 2 billion.
Does this affect the probability that Sally Clark murdered her children?
It might help to consider what would happen in 2 billion random families.
How many of these would have a double murder of children?
In how many of these would two children suffer from SIDS?
In what proportion of families where two children have died were the children murdered?
Sally Clark served three years in prison, before having her convictions overturned.
Lucia de Berk and Hospital Murders
Lucia de Berk, a nurse from the Netherlands, was given a life sentence for the murder or attempted murder of patients in her care in 2003.
Between September 2000 and September 2001, there were 9 unusual deaths in the hospital, which all occurred when Lucia de Berk was on duty.
A statistical calculation was used to "prove" that the probability of her shift coinciding with the deaths of the patients by chance had a probability of $\tfrac{1}{342,000,000}$.
Does this mean that the probability of Lucia being innocent was $\tfrac{1}{342,000,000}$? What else should a jury consider?
See how your thoughts compare to the analysis below:
Lucia de Berk was eventually released, and the Dutch government apologised, in 2010.
Sally Clark and SIDS
The expert, when calculating the probability of two cases of SIDS in the same family, assumed that they were independent, so that the fact that one occurred made it no more likely for the other to occur.
However, SIDS could have either an environmental or a genetic cause. Since the two children were siblings, and lived in the same house, they were likely to be exposed to both the same environment, and have similar genes. This means that the fact that the first child suffered from SIDS makes it more likely that the second one would.
Therefore, assuming that the two cases are independent is not a reasonable assumption.
In a sample of 2 billion random families, you would expect (using the experts statistic) that $\frac{1}{72,250,000} \times 2,000,000,000 \approx 276$ families to have two cases of SIDS.
You would expect one of these families to have both children murdered.
This means there are $277$ families where both children died, of which only one case was by murder. Therefore the probability that Sally Clark murdered her children can be estimated as $\frac{1}{277} \approx 0.4\%$.
Lucia de Berk and Hospital Murders
The jury should also consider what the probability of Lucia de Berk murdering these patients was. Since this is very unlikely, it will increase the chances that all the patients died when she was on duty by chance, using a calculation similar to that used above in the Sally Clark case.
The jury should also consider whether there was any other evidence that Lucia de Berk might have committed the crime. If there is no other evidence, this might be evidence of her innocence.