Question: In 1987 J. Jones was tried for multiple violent crimes. A forensic expert testified that, based on blood samples taken from the crime scene, the assailant had type B blood characteristics and a unique genetic marker. She reported that only 0.32% of the population of the county had these blood characteristics and that Jones had blood type B and the genetic marker. Define the events G and E as

G = Jones is guilty of the crimes

E = Evidence at crime scenes is type B blood and has the genetic marker

As a juror you have heard other circumstantial evidence about the case that makes you think that P(G) = 0.10 (note that this is a subjective probability). Given the forensic evidence, compute the probability that Jones is guilty. While a 10% probability of guilt is not “beyond a reasonable doubt” what do you think about the probability after accounting for the forensic evidence?

Hints:

I. P(E, given G) = 1. If Jones did the crime then the evidence would certainly be type B blood with the genetic marker

II. Argue that P(E, given not G) = 0.0032

III. Use the subjective guilt probability P(G) = 0.10 and the probabilities in the previous two hints to compute P(G, given E), the probability of guilt given the evidence.