Paul and Eric are playing squash, and Paul is determined to win at least two games. Unfortunately his chance of winning any one game is only !, and this chance remains constant however many games he plays against Eric. The players agree to play 5 games and, if Paul has won at least two by then, play ceases. Otherwise Paul persuades Eric to play a further 5 games with him. What is the probability (i) that only 5 games are played, and Paul wins at least two of them; (ii) that 10 games have to be played, and Paul wins at least two?
Paul and Eric are playing squash, and Paul is determined to win at least two games. Unfortunately his chance of winning any one game is only !, and this chance remains constant however many games he plays against Eric. The players agree to play 5 games and, if Paul has won at least two by then, play ceases. Otherwise Paul persuades Eric to play a further 5 games with him. What is the probability (i) that only 5 games are played, and Paul wins at least two of them; (ii) that 10 games have to be played, and Paul wins at least two?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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:Paul and Eric are playing squash, and Paul is determined to win at least two games.
Unfortunately his chance of winning any one game is only !, and this chance remains constant
however many games he plays against Eric. The players agree to play 5 games and, if Paul has
won at least two by then, play ceases. Otherwise Paul persuades Eric to play a further 5 games
with him. What is the probability
(i) that only 5 games are played, and Paul wins at least two of them;
(ii) that 10 games have to be played, and Paul wins at least two?
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