2. 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 finger 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.