There are two systems of the jury. The first is a 1-member jury with a probability p to deliver the correct verdict. The second system is a 3-member jury that works on majority (at least 2) decisions to win. The two members each have an independent probability, p, for making the correct decision, and the third juror flips a coin and decides. Which jury has a better chance of making the right decisions?
Take the case of the 3-member jury:
The probability of getting the majority right = P(all three right) + P(first two correct AND third wrong) + P(first and third right AND second wrong) + P(second and third right AND first wrong)
= p x p x 1/2 + p x p x 1/2 + p x 1/2 x (1-p) + p x 1/2 x (1-p)
= (1/2) x (p2 + p2 + p – p2 + p – p2)
= 2p/2 = p = probability of 1-member jury to make the correct decision.
