Three players, A, B and C, take turns tossing a fair six-sided die in the following sequence: ABC ABC ABC … This continues until one of the players rolls a six. That player then drops out of the game and the others continue until one of them rolls a six, at which point the game ends.  What are the probabilities of the exit sequences AB, BA and CB?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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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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Three players, A, B and C, take turns tossing a fair six-sided die in the following sequence: ABC ABC ABC … This continues until one of the players rolls a six. That player then drops out of the game and the others continue until one of them rolls a six, at which point the game ends. 

What are the probabilities of the exit sequences AB, BA and CB? 

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