Jurors may be a priori biased for or against the prosecution in a criminal trial. Each juror is questioned by both the prosecution and the defense (the voir dire process), but this may not reveal bias. Even if bias is revealed, the judge may not excuse the juror for cause because of the narrow legal de nition of bias. For a randomly selected candidate for the jury, de ne events B0, B1, and B2 as the juror being unbiased, biased against the prosecution, and biased against the defense, respectively. Also let C be the event that bias is revealed during the questioning and D be the event that the juror is eliminated for cause. Let bi P(Bi ) (i 0, 1, 2),C [ Fair Number of Peremptory Challenges in Jury Trials, J. Amer. Statist. Assoc., 1979: 747—753]

a. If a juror survives the voir dire process, what is the probability that he/she is unbiased (in terms of the bi s, c, and d )? What is the probability that he/she is biased against the prosecution? What is the probability that he/she is biased against the defense? Hint: Represent this situation using a tree diagram with three generations of branches. b. What are the probabilities requested in (a) if b0 .50, b1 .10, b2 .40 (all based on data relating to the famous trial of the Florida murderer Ted Bundy), c .85 (corresponding to the extensive questioning appropriate in a capital case), and d .7 (a moderate judge)?