six11 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 displaysa 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 playersselect the same hand signal, the game results in a tie.Two roommates, roommate A and roommate B, are expecting company and are arguing over who should have to wash the dishes before the companyarrives. Roommate A suggests a game of rock-paper-scissors to settle the dispute.Scissorsbeats paperPaperbeats rockRockbeats scissorsConsider the game of rock-paper-scissors to be an experiment. In the long run, roommate A chooses rock 21% of the time, and roommate B choosesrock 61% of the time; roommate A selects paper 39% of the time, and roommate B selects paper 21% of the time; roommate A chooses scissors40% of the time, and roommate B chooses scissors 18% of the time. (These choices are made randomly and independently of each other.)The probabilities were assigned using the relative frequency approachclassical approachDefine event A as the event that roommatbes not have to wash the dishes.subjective approachWhat is P(A), the probability of event A?relative frequency approach What is P(A), the probability of event A?O P(A) = 0.36O P(A) = 0.76O P(A) = 0.22O P(A) = 0.32Let event C be the event that the game ends in a tie.What is P(C), the probability of event C?O P(C) = 0.32O P(C) = 0.28O P(C) = 0.50O P(C) = 0.86Define event B as the event that roommate B wins the game and thus does not have to wash the dishes. What is the probability that roommate B winsthe game?O P(B) = 0.39O P(B) = 0.67O P(B) = 0.36O P(B) = 0.43

Given Information: Let the probability that roomate A chooses rock = PRA=0.21 The probability that roomate A chooses paper = PPA=0.39 The probability that roomate A chooses scissors = PSA=0.40 The probability that roomate B chooses rock = PRB=0.61 The probability that roomate B chooses paper = PPB=0.21 The probability that roomate B chooses scissors = PSB=0.18 (a) Let A be the event that roomate A wins the game and thus does not have to wash the dishes. This will happen only when roomate A chooses rock and roomate B chooses scissors or roomate A chooses paper and roomate B chooses rock or roomate A chooses scissors and roomate B chooses paper. So, PA=PRA×PSB+PPA×PRB+PSA×PPB=0.21×0.18+0.39×0.61+0.40×0.21=0.0378+0.2379+0.084=0.3597≈0.36 Thus, the probability of event A is 0.36 Let C be the event that the game ends in a tie: This will happen only when roomate A chooses rock and roomate B also chooses rock or roomate A chooses paper and roomate B also chooses paper or roomate A chooses scissors and roomate B also scissors. So, PC=PRA×PRB+PPA×PPB+PSA×PSB=0.21×0.61+0.39×0.21+0.40×0.18=0.1281+0.0819+0.072=0.282≈0.28 Thus, the probability of event C is 0.28 Let B be the event that roommate B wins the game and thus does not have to wash the dishes. This will happen only when roommate B chooses rock and roommate A chooses scissors or roommate B chooses paper and roomate A chooses rock or roommate B chooses scissors and roommate A chooses paper. So, PB=PRB×PSA+PPB×PRA+PSB×PPA=0.61×0.40+0.21×0.21+0.18×0.39=0.244+0.0441+0.0702=0.3583≈0.36 Thus, the probability of event B is 0.36