Anand and Kasparov play a suddendeath chess match. Each game ends up With either a Win by Anand with probability p, a Win for Kasparov with probability q, or a draw otherwise with probability (1 = p = q)! independently of the results of prior games. The match continues until one of the players wins a game (and hence the match). (a) (10 points) (b) (10 points) (c) (10 points) What is the probability that Anand Wins the match? ((1) (10 points) Are the events A={Anand wins} and M={The match lasted no more than 5 games} independent? Justify your answer. What is the expected number of games played between the two masters? What is the probability that the match lasts no more than 5 games? Note: The following expressions may be helpful in answering some parts: 00 0 1 0Zak=m, and 0Zk(1a)a(k_1)=1_a. k=0 k=1