Problem 10. Suppose that jury members decide on each case independently, and eac

Question

Problem 10. Suppose that jury members decide on each case independently, and each makes the correct decision randomly with probability p. If the decision of the majority is final, which is preferable in arriving at correct verdicts, a 3-person jury or a single juror? Hint: This will depend on p. For p {0, 1/2, 1 }, it will make no difference. For other cases it will make a difference. Explain carefully how this plays out depending on p and show all the calculations. You need to calculate the probability of a successful decision with a 3-person jury, and compare that with the probability of a correct decision with a single juror (which is just p). When the former is larger than the latter, then the 3-person jury is preferable. That is, assuming you are innocent!

Explanation / Answer

1) Probability of correct decision with 3 jurors = P( 2 jurors make correct)+ P( 3 jurors are correct) = 3C2 * p^2 *(1-p) + p^3 = p^2(3-2p)

For example , if p = 0.6 , Probability of correct decision with 2 jurors = 0.6^2 * (1.8) = 0.648 which is larger than the value of p.

Hence, 3-juror system is preferable for an innocent person.

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