Guilty or innocent? Math in the Courtroom Part II
In 2003, a Dutch nurse named Lucia de Berk was accused of murdering several patients. She was sent to prison for six years in before her conviction was overturned in 2010. The reason for the overturning? The prosecutor and the judges behind the conviction could not do math correctly.
The grade 11 class delved deep into the mathematics given by the prosecution in de Berk’s case and discussed the reasons why it was flawed. The students understood loud and clear that there are some serious implications of not knowing math.
In the hospital where de Berk worked, many patient deaths happened while de Berk was nursing them. The prosecution argued that the chances of de Berk being innocent while all these deaths occurred was incredibly small. However, this probability is not at all the same as the probability of de Berk being innocent, given the evidence.
DNA Match
Let’s look at an example. Suppose that police pick up a suspect and match her DNA to evidence collected at a crime scene. Suppose that the likelihood of a match, purely by chance, is only 1 in 10,000. So, 9,999 times out of 10,000, the DNA match gets it right – isn’t this also the chance of the suspect being guilty? Not at all. Suppose the city in which the person lives has 500,000 adult inhabitants who could have, theoretically, committed the crime. Given the likelihood of a random DNA match, there is about 50 people in the city would seem to have DNA that also matches the sample. So the chance of the suspect being guilty is only 1 out of 50 – this means ‘almost certainly innocent’, quite contrary to the wrong estimate of ‘almost certainly guilty’!
This is more or less what happened with the case of de Berk. It just so happens that patients die – all too frequently, unfortunately – and we shouldn’t be surprised that there are a lot of unlucky nurses who might falsely be blamed for murderer.” (Source: https://www.isutrecht.nl/2017/02/guilty-innocent-math-goes-wrong-courtroom/)
By Mikko Peltonen, DP Mathematical Studies