Roll a fair six-sided die twice. (1) Show by an example based on this experiment that two mutually disjoint events need not be independent.

(2) Let A, B, C be events defined by A = {the sum of the points is 7}, B = {the first roll gives a 3}, C = {the second roll gives a 4}. Show that any two distinct events of these three events are independent, but the three events altogether are not independent in the sense that P(A B C) = P(A)P(B)P(C).