The probability that a three-person jury will make a correct decision is given by where 0 < a < 1 is the probability that the

The probability that a three-person jury will make a correct decision is given by

where 0

(a) Calculate P(0.9, 0.5, 0.6) and P(0.1, 0.8, 0.4) and interpret your answers.
(b) Using common sense and without using calculus, what value of r and s would maximize the jury’s probability of making the correct verdict? Do these values depend on a in this problem? Should they? What is the maximum probability?
(c) Verify your answer for part (b) using calculus.

P(a, r, s) = a[3r(1 r) + r] + (1 - a)[3s(1 - s) + s],