The probability that a three-person jury will make a correct decision is given by
P(α, r, s) = α[3r²(1 - r) + r²] + (1 - α)[3s²(1 - s) + s²],
where 0 < α < 1 is the probability that the person is guilty of the crime, r is the probability that a given jury member will vote "guilty" when the defendant is indeed guilty of the crime, and s is the probability that a given jury member will vote "innocent" when the defendant is indeed innocent. Source: Frontiers of Economics.
a. Calculate P(0. 9, 0. 5, 0. 6) and P(0. 1, 0. 8, 0. 4) and interpret your answers.