Consider four nonstandard dice (the Efron dice), whose sides are labeled as follows (the 6 sides on each die are equally likely). A : 4, 4, 4, 4, 0, 0 B : 3, 3, 3, 3, 3, 3 C : 6, 6, 2, 2, 2, 2 D : 5, 5, 5, 1, 1, 1 These four dice are each rolled once. Let A be the result for die A, B be the result for die B, etc. (a) Find P(A > B), P(B > C), P(C > D), and P(D > A).
(b) Is the event A > B independent of the event B > C? Is the event B > C independent of the event C > D? Explain.