A three-man jury has two members each of whom independently has probability *p* of making the correct decision and a third member who flips a coin for each decision (majority rules). A one-man jury has the probability *p* of making the correct decision. Which jury has the better probability of making the correct decision (the 3-member jury or the one-member jury)?

Let A, B, C be the jurors and let A be the one who flips the coin. Different probabilities can be represented using the tree diagram below:

The probability that the three member jury takes a correct decision is the following sum:

(1)/(2)⋅*p*⋅*p* + (1)/(2)⋅*p*⋅(1 − *p*) + (1)/(2)⋅(1 − *p*)⋅*p* + (1)/(2)⋅(1 − *p*)⋅(1 − *p*) = *p*^{2} + *p*(1 − *p*) = *p*.

So, we conclude that both juries have the same probabil;ity *p*.