Question

The prosecutor's fallacy is misunderstanding or confusion of two different conditional probabilities: (1) the probability that a defendant is innocent, given that forensic evidence shows a match; (2) the probability that forensics shows a match, given that a person is innocent. The prosecutor's fallacy has led to wrong convictions and imprisonment of some innocent people. Lucia de Berk is a nurse who was convicted of murder and sentenced to prison in the Netherlands. Hospital administrators observed suspicious deaths that occurred in hospital wards where de Berk had been present. An expert testified that there was only one chance in 342 million that her presence was a coincidence. However, mathematician Richard Gill calculated the probability to be closer to 1/50, or possibly as low as 1/5. The court used the probability that the suspicious deaths could have occurred with de Berk present, given that she was innocent. The court should have considered the probability that de Berk is innocent, given that the suspicious deaths occurred when she was present. This error of the prosecutor's fallacy is subtle and can be very difficult to understand and recognize, yet it can lead to the imprisonment of innocent people.

What are your thoughts on this? Does the distinction between the two conditional probabilities make sense? Do you have questions for the expert or mathematician?

Answer 1

The two probabilities are as follows:

P(The defendant is innocent | Thr forensic evidence shows a match)

and

P( The forensic evidence shows a match | The person is innocent)

The above two probabilities are not necessarily the same. The first probability gives the chance that the defendant is innocent given that the evidence shows a match. The second probability gives the probability that the forensic evidence will show a match even when the defendant is innocent.

The case presented shows how the two probabilities can be alternated when arriving at a decision. The court sed the probability that the suspicious deaths could have occurred with de Berk present, given that she was innocent however the right probability to consider would have been to judge the probability that the nurse is innocent, given that the suspicious deaths occurred when she was present.

The above presents a case of the wrong statistical reasoning to argue the case. The above decisions are based on the assumption that the chance of finding evidence of guilt against an innocent man is so less that it is plausible to disregard the possibility that the defendant is innocent. The false belief obscures that the percentages of a defendant being innocent given same proof, of course, depends on the likely higher previous odds of the defendant being innocent, the expressly lesser odds of the proof within the case that he was innocent as mentioned, further because the underlying additive odds of the proof being on the defendant.

The new probability as calculated by the mathematician needs proper authentication. The mathematician should provide proper reasonng behind the newly calculated probability that the nurse's presence was a coincidence. The calculated fgure needs proper validation through a detailed presentation of facts.