A three-man jury has two members each of whom independently has probability of making the correct decision and a third member who flips a coin for each decision (majority rules) A one-man jury has probability of making the correct decision. Which jury has the better probability of making the correct decision? 1
The winning outcomes for the first scenario (three juris) are:
Hence, the probability of a correct decision is given by:
The two scenarios are strictly equivalent.
Half the times the flippant member agrees with the first member. In these cases the conditional probability of a correct decision is . The other half it agrees with the second member, where the conditional probability is also , thus .