A table tennis match is played between Jack and Rose. The winner of the match is...

A table 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.

Expert Solution

orchestra answered 2 years ago

betting theory on tennis A bookmaker has quoted odds on a tennis match between players I...

betting theory on tennis A bookmaker has quoted odds on a tennis match between players I and II. The match consists of the best two out of three sets, i.e., if a player wins the first two sets, the third set is not played and the bet on it is canceled. The bookmaker is giving odds of 5 to 2 that player I will win the match and odds of 3 to 2 that player I will win each set....

Rose and Jack plan to study together for the AMS311 test. They decide to meet at...

Rose and Jack plan to study together for the AMS311 test. They decide to meet at the library between 8:00pm and 8:30pm. Assume that they each arrive (independently) at a random time (uniformly) in this interval. It is possible that someone has to wait up to 30 minutes for the other to arrive. a). What is the probability that someone (Rose or Jack, whichever arrives ﬁrst) must wait more than 20 minutes until the other one arrives? What is the...

11. Rose and Jack plan to study together for the AMS311 test. They decide to meet...

11. Rose and Jack plan to study together for the AMS311 test. They decide to meet at the library between 8:00pm and 8:30pm. Assume that they each arrive (independently) at a random time (uniformly) in this interval. It is possible that someone has to wait up to 30 minutes for the other to arrive. a). What is the probability that someone (Rose or Jack, whichever arrives ﬁrst) must wait more than 20 minutes until the other one arrives? What is...

In a tennis match, the first serve percentage is a key statistic. Having an accurate (and...

In a tennis match, the first serve percentage is a key statistic. Having an accurate (and fast) first serve is seen as an important advantage to winning a match. Let theta be the probability of getting the first serve in on any point in a tennis game. For each of the four situations below, give a prior distribution for theta, explaining each in a sentence. You may assume the winner is determined from the best of three sets, (so the...

During a tennis match, a player serves the ball at 28.6 m/s, with the center of...

During a tennis match, a player serves the ball at 28.6 m/s, with the center of the ball leaving the racquet horizontally 2.33 m above the court surface. The net is 12.0 m away and 0.900 m high. When the ball reaches the net, (a) what is the distance between the center of the ball and the top of the net? (b) Suppose that, instead, the ball is served as before but now it leaves the racquet at 5.00° below...

During a tennis match, a player serves the ball at 25.6 m/s, with the center of...

During a tennis match, a player serves the ball at 25.6 m/s, with the center of the ball leaving the racquet horizontally 2.34 m above the court surface. The net is 12.0 m away and 0.900 m high. When the ball reaches the net, (a) what is the distance between the center of the ball and the top of the net? (b) Suppose that, instead, the ball is served as before but now it leaves the racquet at 5.00° below...

3.17 You and I play a tennis match. It is deuce, which means if you win...

3.17 You and I play a tennis match. It is deuce, which means if you win the next two rallies, you win the game; if I win both rallies, I win the game; if we each win one rally, it is deuce again. Suppose the outcome of a rally is independent of other rallies, and you win a rally with probability p. Let W be the event “you win the game,” G “the game ends after the next two rallies,”...

ALL LEASES BELOW ARE BETWEEN LUNA AND JACK A. On January 1, 2021, Jack leased office...

ALL LEASES BELOW ARE BETWEEN LUNA AND JACK A. On January 1, 2021, Jack leased office space from Luna under a 20-year operating lease agreement. Luna’s borrowing rate is 5%. The lease calls for annual lease payments of $10,000 on January 1 of each year. Record all journal entries related to the lease for 2021, 2022, and 2023 for both Luna and Jack. B. On January 1, 2021, Jack leased a catnip processing factory for a 4-year period ending December...

Chapter 04, Problem 036 During a tennis match, a player serves the ball at 25.5 m/s,...

Chapter 04, Problem 036 During a tennis match, a player serves the ball at 25.5 m/s, with the center of the ball leaving the racquet horizontally 2.55 m above the court surface. The net is 12.0 m away and 0.900 m high. When the ball reaches the net, (a) what is the distance between the center of the ball and the top of the net? (b) Suppose that, instead, the ball is served as before but now it leaves the...

1. Who is the winner and loser between consumer and producer, when the price floor is...

1. Who is the winner and loser between consumer and producer, when the price floor is implemented? 2. Who is the winner and loser between consumer and producer, when the price ceiling is implemented?

Question