Qusetion: Suppose that in order for the defendant to be convicted in a military court the majority of the nine appointed judges must enter a guilty vote. Assume that a judge enters a guilty vote with probability 0.1 or 0.9 if the defendant is innocent or guilty, respectively, independently of other judges. Assume also that 40% of the defendants in such trials are innocent.
(a) What proportion of all defendants is convicted?
(b) What is the proportion of correct verdicts?