Math Problem Statement
Three individuals, labelled A, B, and C, engage in a dice game using a standard sixsided die. They roll the die in a repeating sequence: A, then B, then C, followed by A, B, C, and so on. The game continues until one player rolls a six, at which point they are eliminated. The remaining two players then continue the process until one of them also rolls a six, ending the game. What are the probabilities for each of A, B and C to be the first to exit the game? Hint: Think carefully about what can happen at each step for A to find the probability A exits first, then consider B and C in turn. The following formula for a geometric sum may be useful.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Geometric Series
Game Theory
Formulas
Geometric series sum formula
Theorems
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Suitable Grade Level
Advanced High School