A common way for two people to settle a frivolous dispute is to play a game of r

Question

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 beat 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-scissors to settle the dispute. 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 B 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 B believes that there is a 0.17 probability that his roommate will choose rock and a 0.39 probability that his roommate will choose paper. The probabilities are assigned using the Suppose that roommate B's probability you say about P(Sa), the probability that roommate A chooses scissors? Check all that apply. classical approach subjective approach relative frequency approach P(S_A) = 0.31 0 lessthanorequalto P(S_A) lessthanorequalto 0.1 P(S_A) = 0.44 1 lessthanorequalto P(S_A) lessthanorequalto 2 P(S_A) = 0.13 Assume that roommate B's probability assignments are correct. Roommate B would like to use the hand signal with the highest probability of winning the game. What would you advise roommate B to use? You can simulate a play of the game by basing the game's result on roommate B's probability assignments. That is, the chance that roommate A chooses rock is P(R_A), the chance that he chooses paper is P(P_A), and the chance that he chooses scissors Is P(S_A), where P(R_A), P(P_A), and P(S_A) have been previously determined. Okay, play it now! (Click the red PLAY! icon to reveal roommate A's choice.) If roommate B took the advice to choose the highest probability of winning, then roommate B __ the game.

Explanation / Answer

a)Since P(S) + P(R )+ P(P) = 1

and P(R) =0.39

P(P)=0.17

=>P(S) = 0.44

I would advice B to choose paper , because A knows the maximum probability that B will chose is Scissors, so A will chose rock, hence in order to win B has to chose paper

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