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In a game, a player wins or loses one point at each trial with probabilities 0.75 and 0.25 respectively. The game terminates whenever his score reaches +2 or -2. He wins the game if the score is +2 and loses if the score is -2. Let p be the probability that he wins the game, q be the conditional probability that he wins the game when it is known that he has won the first trial, and r be the conditional probability that he wins the game when it is known that he has lost the first trial. (a) (i) Show that q = 0.75 + 0.25p. (ii) Set up two more equations relating p, q and r and hence solve for p, q and r. (b) Find the probability that the game will terminate at the end of the n-th trial, (i) if n is odd, and (ii) if n is even. (c) Find the expected number of trials for each game