Suppose that Dirty Harry is on trial for Crimes Against Prob

Suppose that Dirty Harry is on trial for Crimes Against Probability, and at the trial, the jury members decide independently and that each juror makes the correct decision with probability p. If the decision of the majority is final, the question is, which would be preferable for a correct outcome at the end of the trial, to have a single juror, or a 3-person jury?

(a) For what probability p does this not make a difference?

(b) For what probabilities p is is preferable to have a 3-person jury?

(c) For what probabilities p is is preferable to have a single juror?

[Hint: Consider the probability p\' for the binomial B(3,p) for the case of 2 or 3 successes and compare with p.]

Solution