9. Rock-paper-scissors #2 Aa Aa A common way for two people to settle a frivolou
ID: 3356542 • Letter: 9
Question
9. Rock-paper-scissors #2 Aa Aa A common way for two people to settle a frivolous dispute is to play a game of rock-paper-scissors. In this game, each person simultaneously displays a hand signal to indicate a rock, a piece of paper, or a pair of scissors. Rock beats scissors, scissors beats paper, and paper beats rock. If both players select the same hand signal, the game results in a tie Scissors beats paper Paper beats rock Two roommates, roommate A and roommate B, are expecting company and are arguing over who should have to wash the dishes before the company arrives. Roommate A suggests a game of rock-paper-scissors to settle the dispute Rock beats scissors Consider the game of rock-paper-scissors to be a random circumstance. In the long run, roommate A chooses rock 36% of the time, and roommate B chooses rock 22% of the time; roommate A selects paper 32% of the time, and roommate B selects paper 25% of the time; roommate A chooses scissors 32% of the time, and roommate B chooses scissors 53% of the time. (These choices are made randomly and independently of each other.) The probabilities were assigned using the personal probability interpretation . Define event A as the event that roommate A wins the game and thus does not have to wash the dishes. What is P(A), the probability of event A? P(A)-0.38 P(A) 0.34 P(A) = 0.76 P(A) = 0.32 O Let event C be the event that the game ends in a tie What is P(C), the probability of event C? P(C) = 0.32 P(C) = 0.44 P(C) = 0.33 P(C) o.55 OExplanation / Answer
Here probability of A winning the game is
Pr(A) = Pr(A chooses rock) * Pr(B Chooses scissors) + Pr(A chooses scissors) * Pr(B chooses Paper) + Pr(A chooses Paper) * Pr(B chooses rock)
= 0.36 * 0.53 + 0.32 * 0.25 + 0.32 * 0.22
= 0.3412 [Option B is correct]
Here Event P(C) is the event of tie. A tie will occur when both will show the same type of options to each other.
Pr(C) = Pr(A shows rock) * Pr( B shows Rock) + Pr(A shows paper) * Pr(B shows paper) + Pr(A shows scissors) * Pr(B shows scissors)
= 0.36 * 0.22 + 0.32 * 0.25 + 0.32 * 0.53
= 0.3288
Option C is correct.
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