1. Hank and Vernon will play a best-of-three horseshoe-pitching match. (The first pitcher to win two games wins the match.) Hank has probability ¾ of winning each game, independent of the history. (i) What is the probability that the match ends after two games? (ii) If a third game is needed, what is the probability that the winner of the second game will win the third?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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1. Hank and Vernon will play a best-of-three horseshoe-pitching match. (The first pitcher to
win two games wins the match.) Hank has probability ¾ of winning each game, independent of
the history.
(i) What is the probability that the match ends after two games?
(ii) If a third game is needed, what is the probability that the winner of the second game will win
the third?
Transcribed Image Text:1. Hank and Vernon will play a best-of-three horseshoe-pitching match. (The first pitcher to win two games wins the match.) Hank has probability ¾ of winning each game, independent of the history. (i) What is the probability that the match ends after two games? (ii) If a third game is needed, what is the probability that the winner of the second game will win the third?
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