Jim and Renjee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renjee have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?
Select the correct option:
A) 5/6
B) 2/3
C) 1/2
D) 5/12
E) 1/3
1/3   probability of jim winning is basically the sum of three probabilities:   probability of jim picking rock and renjee picking scissors = 1/3*1/3 = 1/9   probability of jim picking scissors and renjee picking paper = 1/3*1/3=1/9   probability of jim picking paper and renjee picking rock = 1/3*1/3=1/9   1/9 + 1/9 + 1/9 = 3/9 = 1/3=1/3
<result>E</result>
Jim and Renjee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renjee have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?