Jim and Renee will play one game of Rock, Paper, Scissors. In this game,

BTGModeratorVI wrote: ↑

Sat Jun 27, 2020 6:41 am

Jim and Renee 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 Renee have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?

A. 5/6
B. 2/3
C. 1/2
D. 5/12
E. 1/3

Answer: E
Source: Manhattan prep

Here's another way to look at it.
Let's say that Renee already knows what she is going to select. So, that part is done.

At this point, what are the possible outcomes?
a) Jim selects the one sign that allows him to win
b) Jim selects the one sign that allows Renee to win
c) Jim selects the one sign that results in a tie.

Since each of these outcomes is equally likely, the probability of each outcome is 1/3
So, the probability that Jim wins is 1/3

Answer: E

BTGModeratorVI wrote: ↑

Sat Jun 27, 2020 6:41 am

Jim and Renee 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 Renee have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?

A. 5/6
B. 2/3
C. 1/2
D. 5/12
E. 1/3

Answer: E
Source: Manhattan prep

Solution:

We can make a table that tabulate the results from Jim’s point of view: We see that Jim wins 3 out of 9 times, therefore, the probability he wins is 3/9 = 1/3.

Alternate Solution:

Since each player has three choices of hand signs, the total number of pairs of hand signs the two players can show is 3 x 3 = 9. Of these 9 possibilities, Jim wins in 3 of them (which are S-P, P-R and R-S where the first letter is Jim’s pick). Thus, the probability that Jim wins is 3/9 = 1/3.

Answer: E