Suppose that the birthday of each of three people is equally likely to be any one of the 365 days of the year, independently of others. Let B(sub ij) denote the event that person i has the same birthday as person j, where the labels i and j may be 1, 2, or 3.

a) Are the events B(sub 12) and B(sub 23) independent?

b) Are the events B(sub 12), B(sub 23), and B(sub 13) independent?

C) Are the events B(sub 12), B(sub 23), and B(sub 13) pairwise independent?