Rock smashes scissors Almost everyone has played the rock-paper- scissors game at some point. Two players face each other and, at the count of 3, make a fist (rock), an extended hand, palm side down (paper), or a "V" with the index and middle fingers (scissors). The winner is determined by these rules: rock smashes scissors; paper covers rock; and scissors cut paper. If both players choose the same object, then the game is a tie. Suppose that Player 1 and Player 2 are both equally likely to choose rock, paper, or scissors. (a) Give a probability model for this chance process. (b) Find the probability that Player 1 wins the game on the first throw. 3.

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Rock smashes scissors Almost everyone has played the rock-paper-
scissors game at some point. Two players face each other and, at the count
of 3, make a fist (rock), an extended hand, palm side down (paper), or a
"V" with the index and middle fingers (scissors). The winner is
determined by these rules: rock smashes scissors; paper covers rock; and
scissors cut paper. If both players choose the same object, then the game is
a tie. Suppose that Player 1 and Player 2 are both equally likely to choose
rock, paper, or scissors.
(a) Give a probability model for this chance process.
(b) Find the probability that Player 1 wins the game on the first throw.
3.
Transcribed Image Text:Rock smashes scissors Almost everyone has played the rock-paper- scissors game at some point. Two players face each other and, at the count of 3, make a fist (rock), an extended hand, palm side down (paper), or a "V" with the index and middle fingers (scissors). The winner is determined by these rules: rock smashes scissors; paper covers rock; and scissors cut paper. If both players choose the same object, then the game is a tie. Suppose that Player 1 and Player 2 are both equally likely to choose rock, paper, or scissors. (a) Give a probability model for this chance process. (b) Find the probability that Player 1 wins the game on the first throw. 3.
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