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. On a given evening, two roommates, roommate A and roommate B, are arguing over who should control the television remote. Roommate A suggests a game of rock-paper-seissors to settle the dispute. Scissors beats paper Paper beats rock Rock beats scissors It's the first time that the roommates have played each other in rock-paper-scissors, so there is no history of the choices made by either roommate. However, roommate A thinks that the three possibilities for his roommate's choice of hand signal are not equally likely. Based on his roommate's behavior in other similar games, roommate A believes that there is a 0.28 probability that his roommate will choose rock and a 0.61 probability that his roommate will choose paper. The probabilities are assigned using the Poduction to Probability Suppose that roommate A's probability assignments are correct. What can you say about P( S ), the probability that roommate B chooses scissors? Check all that apply. O P(Sa ) = 0.11 OO S P( S ) s 0.1 D1 P( Sp ) s 2 O P( SB) = 0.13 OOS P( Sa ) s 1 Assume that roommate A's probability assignments are correct. Roommate A would like to use the hand signal with the highest probability af winning the game. What would you advise roommate A to use? You can simulate a play of the game by basing the game's result on roommate A's probability assignments. That is, the chance that roommate B chooses rock is P(Rn ), the chance that he chooses paper is P(Pa ), and the chance that he chooses scissors is P(Sp ), where P(Rp ), P( P ). and P( Sn ) have been previously determined. Okay, play it now! (Click the blue PLAYI icon to reveal roommate B's choice.) PLAYI the game. If roommate A took the advice to choose the highest probability of winning, then roommate A