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.

a) Let's suppose that player 1 chooses rock, and the selection of player 2 can be thought as random.

If player 2 randomly selects rock, the result of the game is a draw.

if player 2 randomly selects papers, player 1 loses.

if player 2 randomly selects scissors, player 1 wins.

Then we have 3 options with the same probability, that will be:

1/3

This is, the probability of winning is equal to the quotient between the number of outcomes that make player one win (1, in this case, scissors) and the total number of outcomes (3) = 1/3

the probability of a draw is equal to the quotient between the number of outcomes that make a draw (1, in this case, rock) and the total number of outcomes (3) = 1/3

the probability of losing is equal to the quotient between the number of outcomes that make player one lose (1, in this case, paper) and the total number of outcomes (3) = 1/3

And remember that this will be the same for any selection of the player 1.

b) As we already found, the probability of winning for any selection is 1/3 = 0.333..

55

step-by-step explanation: