Suppose each of three persons tosses a coin. If the outcome of one of the tosses differs from the other outcomes, then the game ends. If not, then the persons start over and retoss their coins. Assuming fair coins, what is the probability that the game will end with the at most second round of tosses?
Probability question
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Dr.Peterson
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Have you tried making a tree representing the possible outcomes?
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pka
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Here is a list of the possible outcomes on each round.
\(\begin{array}{*{20}{c}} H&H&H \\ H&H&T \\ H&T&H \\ H&T&T \\ T&H&H \\ T&H&T \\ T&T&H \\ T&T&T \end{array}\)
What is the probability the game is over in one round?
What is the probability the game is over in two rounds?