Question

6. Defining probability terms using rock-paper-scissors

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 whether the music should be turned down. Roommate A suggests a game of rock-paper-scissors to settle the dispute.

Assuming that these roommates play fairly and use only one of the three hand gestures, the following notation describes the possible events:

Roommate A believes it is equally likely that Roommate B will show any of the three hand gestures. In other words, she believes that p(RB)=p(Pθ)=p(SB)=_______ 

On the other hand, Roommate B has recorded Roommate A's gestures every time they have played this game. (Unfortunately, they argue a lot, so Roommate B has a lot of data.) Based on her data, Roommate B believes there is a 0.20 probability that Roommate A will show rock [in other words, \left.p(R_{A})=0.20\right] and a 0.65 probability that Roommate A will show paper [in other words, p(PA)=0.65].

Answer 1

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