Two players play each other in a pool tournament of \"Solids and Stripes\". The first player...

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Two players play each other in a pool tournament of \"Solids andStripes\". The first player to win two games wins the tournament. Inthe game of \"Solids and Stripes\", it is equally likely that aplayer will be assigned solid balls or striped balls. Assume that1) one-half of the balls are solids and the other half are stripes,2) the two players have the same skill: each with a 0.5 probabilityof winning, 3) there are no ties, and 4) the tournament isconcluded once a player has won two games. In a tournament, what isthe probability that a player is assigned the same ball design(i.e., solids or stripes) throughout the tournament?

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As there are no ties in the games there can be a maximum of three games between the two players The results can be as follows X Winners Game 1 Game 2 Game 3 PX PY Y Same Ball Design See Answer

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