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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Thu Aug 27, 2020 12:12 pm

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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

Source: Beat The GMAT — Problem Solving | Thu Aug 27, 2020 12:12 pm

dg1900: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Aug 26, 2020 9:45 am

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

by dg1900 » Fri Aug 28, 2020 1:24 am

This question can be solved using combinatorics.

Total possible number of combinations which can be played by Jim and Renee would be:
(Types of move Jim can play) * (Types of move Renee can play)
3 * 3 = 9

The number of combinations in which Jim wins is:
1) Jim plays rock and Renee place scissors
2) Jim pays paper and Renee plays Rock
3) Jim plays scisssors and Renee plays paper

Therefore, the probability of Jim winning will be:

$$\frac{3}{9}=\frac{1}{3}$$

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

by Scott@TargetTestPrep » Mon Aug 31, 2020 11:47 am

BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:12 pm
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

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

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

by Brent@GMATPrepNow » Wed Sep 02, 2020 9:50 am

BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:12 pm
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

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