Suppose you play a game with a (fair) six sided die, with sides 1, 2, 3, 4, 5, 6. The first time you roll, whatever you roll becomes the "set". If the set is a 6, you win (and you stop rolling). If the set is anything other than 6, the set becomes the new "mark". You then keep rolling until you either roll above the mark, in which case your lose (and you stop rolling), or you roll the mark, in which case the new mark becomes one plus the old mark, and you repeat this process. Whenever the mark becomes 6, you win (and you stop rolling). Calculate the probability that you win this game.

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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Suppose you play a game with a (fair) six sided die, with sides 1, 2, 3, 4, 5, 6. The first time you
roll, whatever you roll becomes the "set". If the set is a 6, you win (and you stop rolling). If
the set is anything other than 6, the set becomes the new "mark". You then keep rolling until
you either roll above the mark, in which case your lose (and you stop rolling), or you roll the
mark, in which case the new mark becomes one plus the old mark, and you repeat this process.
Whenever the mark becomes 6, you win (and you stop rolling). Calculate the probability that
you win this game.
Transcribed Image Text:Suppose you play a game with a (fair) six sided die, with sides 1, 2, 3, 4, 5, 6. The first time you roll, whatever you roll becomes the "set". If the set is a 6, you win (and you stop rolling). If the set is anything other than 6, the set becomes the new "mark". You then keep rolling until you either roll above the mark, in which case your lose (and you stop rolling), or you roll the mark, in which case the new mark becomes one plus the old mark, and you repeat this process. Whenever the mark becomes 6, you win (and you stop rolling). Calculate the probability that you win this game.
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