Consider n people and suppose that each of them has a birthday that is equallylikely to be any of the 365 days of the year. Furthermore, assume that theirbirthdays are independent, and let A be the event that no two of them share thesame birthday. Define a trial for each of the n2pairs of people and say that trial(i, j), i 6= j, is a success if persons i and j have the same birthday. Let Si,j be theevent that trial (i, j) is a success.

(a) Find Pr(Si,j ), i 6= j.

(b) Are Si,j and Sk,r independent when i, j, k, r are all distinct?

(c) Are Si,j and Sk,j independent when i, j, k are all distinct?