(a) Your initial belief is that a defendant in a court case is guilty with probability 0.5. A witness comes forward claiming he saw the defendant commit the crime. You know the witness is not totally reliable and tells the truth with probability p. Use Bayes’ theorem to calculate the posterior probability that the defendant is guilty, based on he witness’s evidence.

(b) A second witness, equally unreliable, comes forward and claims she saw the defendant commit the crime. Assuming the witnesses are not colluding, what is your posterior probability of guilt?

(c) If p < 0.5, compare the answers to (a) and (b). How do you account for this curious result?