A witness testifies that there are about 10 million men who could have been the perpetrator of a particular heinous crime. The probability of a randomly selected man having a DNA profile that is identical with the trace recovered from the crime scene is approximately 0.0001%. If a man does not have this DNA profile, current DNA technology leads to a reported match with probability of only 0.001%. A match between the DNA of the defendant and the traces on the victim has been reported.
a) What is the probability that the reported match is a true match, that is, that the person actually has this DNA profile?
b) What is the probability that the person is the source of the trace?
c) Render a verdict for this case: Guilty or not guilty?