(a) Tenuka and Olivia enjoy playing a particular game for two players. The game always results in one winner and one loser so that the game can never end in a draw. When they play the game, the probability that Tenuka wins is 0.6. They decide to play a tournament in which they will play the game multiple times. The tournament will continue until one of the players has won five games more than the other player. (i) Explain why this tournament could be considered as a Gambler's ruin problem played between Tenuka and Olivia each starting with £5 with the loser passing the winner £1 in each round. (ii) Hence calculate the probability that in any tournament, Olivia is declared the winner. (iii) Find the average number of games played in any tournament.
(a) Tenuka and Olivia enjoy playing a particular game for two players. The game always results in one winner and one loser so that the game can never end in a draw. When they play the game, the probability that Tenuka wins is 0.6. They decide to play a tournament in which they will play the game multiple times. The tournament will continue until one of the players has won five games more than the other player. (i) Explain why this tournament could be considered as a Gambler's ruin problem played between Tenuka and Olivia each starting with £5 with the loser passing the winner £1 in each round. (ii) Hence calculate the probability that in any tournament, Olivia is declared the winner. (iii) Find the average number of games played in any tournament.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:(a) Tenuka and Olivia enjoy playing a particular game for two players.
The game always results in one winner and one loser so that the
game can never end in a draw. When they play the game, the
probability that Tenuka wins is 0.6.
They decide to play a tournament in which they will play the
game multiple times. The tournament will continue until one of
the players has won five games more than the other player.
(i)
Explain why this tournament could be considered as a
Gambler's ruin problem played between Tenuka and Olivia
each starting with £5 with the loser passing the winner £1 in
each round.
(ii) Hence calculate the probability that in any tournament,
Olivia is declared the winner.
(iii) Find the average number of games played in any tournament.
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