Atable tennis match is played between jack and rose. the winner of the match is the one who first wins 4 games in total, and in any game the winner is the one who first scores 11 points. note that in an individual game, if the score is 10 to 10, the game goes into extra play (called deuce) until one player has gained a lead of 2 points. let p be the probability that rose wins a point in any single round of serve, and assume that different rounds in all games are independent. (i) how many games can there be at most before a match winner appears? (ii) in a given individual game, what is the probability that the game runs into the deuce stage? (iii) suppose that p=0.6. compute the probability that rose wins the match? (iv) as a function of p, let f(p) be the probability that the match ends with a maximal number of games. for what value(s) of p is f(p) largest? justify your answer and compute the resulting probability.