5.61 DNA evidence compelling? DNA evidence can be extracted from biological traces such as blood, hair, and saliva. “DNA fingerprinting” is increasingly used in the courtroom as well as in paternity testing. Given that a person is innocent, suppose that the probability of his or her DNA matching that found at the crime scene is only 0.000001, one in a million. Further, given that a person is guilty, suppose that the probability of his or her DNA matching that found at the crime scene is 0.99. Jane Doe’s DNA matches that found at the crime scene.

a. Find the probability that Jane Doe is actually innocent, if absolutely her probability of innocence is 0.50. Interpret this probability. Show your solution by introducing notation for events, specifying probabilities that are given, and using a tree diagram to find your answer.

b. Repeat part a if the unconditional probability of innocence is 0.99. Compare results.

c. Explain why it is very important for a defense lawyer to explain the difference between P1DNA match •

person innocent2 and P1person innocent•DNA match2.