In the game of Problem 57, what is the probability that there will be an odd man

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In the game of Problem 57, what is the probability that there will be an odd man out in a particular play if there are five players?

Data from Problem 57

In a certain office, three men determine who will pay for coffee by each flipping a coin. If one of them has an outcome that is different from the other two, he must pay for the coffee. What is the probability that in any play of the game there will be an "odd man out"?

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