Let 4 persons play the game of odd man out with fair coins, Basic Statistics

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Let 4 persons play the game of odd man out with fair coins

Let 4 persons play the game of "odd man out" with fair coins. What is the probability, for n = 1, 2, ... , that n plays will be required to conclude the game (that is, the nth play is the first play on which I of the players will have an outcome on his coin toss that is different from those of all the other players)?

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