Jay and Maurice are playing a tennis match. In one particular game, they have reached deuce, which means each player has won three points. To finish the game, one of the two players must get two points ahead of the other. For example, Jay will win if he wins the next two points (JJ), or if Maurice wins the next point and Jay the three points after that (MJJJ), or if the result of the next six points is JMMJJJ, and so on. a. Suppose that the probability of Jay winning a point is .6 and outcomes of successive points are independent of one another. What is the probability that Jay wins the game? [Hint: In the law of total probability, let AI = Jay wins each of the next two points, A2 = Maurice wins each of the next two points, and A3 = each player wins one of the next two points. Also let p = P(Jay wins the game). How does p compare to P(Jay wins the game I A3)?] b. If Jay wins the game, what is the probability that he needed only two points to do so?

Answer: Step1: Given that, Jay and Maurice are playing a tennis match. In one particular game, they have reached deuce, which means each player has won three points. To finish the game, one of the two players must get two points ahead of the other. For example, Jay will win if he wins the next two points (JJ), or if Maurice wins the next point and Jay the three points after that (MJJJ), or if the result of the next six points is JMMJJJ, and so on. Step2: a). Given that, Probability of Jay winning a point is P(A 1 = 0.6 Probability that Maurice wins a point is P(A ) = 0.4. 2 To find the probability that Jay wins the game. Jay requires two additional points to win the game. P(jay) = P(A )1+ P(A ) 2 P(A A 1 2 = P(A ) + P(A ) P(A ) .P(A ) 1 2 1 2 = (0.6) + (0.4) 0.6 0*4 P(jay) = 0.76 Therefore, the probability that Jay wins the game is 0.76. Step3: b). Given that if Jay wins the game. The aim is to find the probability that he needed only two points. 0.6×0.6 P(needed two points/jay won the game) = 0.76 = 0.36 0.76 = 0.4736 0.5 Therefore, the probability that he needed only two points is 0.5. Hence proved.