# 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:

*Mark Buchanan, Statistics: conviction by numbers (Nature 2007)*

*Lucia de Berk was eventually released, and the Dutch government apologised, in 2010.*