Jim and Renee will play one game of...

[ameya]

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

Ans: E

The explaination to the above question is: No matter what sign Jim throws, there is one sign Renee could throw that would beat it, one that would tie, and one that would lose. Renee is equally likely to throw any one of the three signs. Therefore, the probability that Jim will win is 1/3.

However, this explaination seems incorrect. If we say the probability of Jim to win is 1/3 and that of Renee to win is 1/3, then what is the remaining 1/3 probability for?
I thought the answer is 1/2.

[Guest]

Tricky question, but I think the solution is:

Probability of choosing either a rock, paper, or scissor is 1/3 each.

R>S
S>P
P>R

The 3 scenarios where Jim will win this one game of rock, paper, scissors is:

Jim picks Rock, AND Renee picks Scissors. (1/3 * 1/3) = 1/9
Jim picks Scissors, AND Renee picks Paper. (1/3 * 1/3) = 1/9
Jim picks Paper, AND Renee picks Rock. (1/3 * 1/3) = 1/9

The 1st scenario OR the 2nd scenario OR the 3rd scenario will allow Jim to win his one game of rock, paper, scissors. So,

1/9 + 1/9 + 1/9 = 3/9 = 1/3

[rfernandez]

Answering ameya's question:

P(Jim wins) = 1/3
P(Renee wins) = 1/3
P(They tie) = 1/3

Rey

[aps_asks]

Hi instructors ,

Can you confirm that the above answer provided by guest on Sat May 31, 2008 12:25 pm is correct or not ?

[jnelson0612]

Hi instructors ,

Can you confirm that the above answer provided by guest on Sat May 31, 2008 12:25 pm is correct or not ?

Guest is correct. That is the more complicated way to do the problem; the post by Rey Fernandez directly above this one is the simpler way to conceptualize the problem.

[aps_asks]

Thanks!

[tim]

:)

[sadaf.marefat]

You are wrong I think!.

In the stimulus there is no sign of definition of "TIE" situation! this comes from your experience in real world not from stimulus.
So the probability of losing is not 1/3 it becomes 2/3.(in the stimulus it had mentioned that just 1 situation of them game is wining situation so the other situations must be loosing situation as there is no explanation of tie situation)!


This means the probability becomes: 1C3 * 1/3*2/3=2/3

[tim]

i think you're not reading the question correctly. keep in mind the concept of a tie is implicit in the definition of the game, and the problem is asking for the probability of a win..

[sadaf.marefat]

Then you have an assumption that anybody in the world knows the "Tie " rule for this game out of the stimulus!

[tim]

no, not at all. again, please read the problem. there is no requirement to distinguish between a loss and a tie, as the only thing we are concerned about here is how a win is defined and what the probability of winning is..

[amycompton]

That is the more complicated way to do the problem; the post by Rey Fernandez directly above this one is the simpler way to conceptualize the problem.

[tim]

Amy, this is the second time you've created a post that consists of nothing more than quoting an instructor's words as your own in a totally irrelevant context. If you do this again, I will have you banned from the forums. Please make some effort to contribute to the discussion rather than just wasting bandwidth..

[tim]

you're right that we don't need to talk about ties; instead, let's just talk about winning and "not winning" (which includes losing or tying). that will greatly simplify the problem..

[nimathur]

Shouldnt it be this?

Jim picks Rock, AND Renee picks Scissors. (1/3 * 1) = 1/3
Jim picks Scissors, AND Renee picks Paper. (1/3 * 1) = 1/3
Jim picks Paper, AND Renee picks Rock. (1/3 * 1) = 1/3

Reason for "1". If Jim picks rock, Renee has only 1 option in order to make Jim win, which is to pick Scissor and hence probability of 1 for Renee.

Thanks.

Tricky question, but I think the solution is:

Probability of choosing either a rock, paper, or scissor is 1/3 each.

R>S
S>P
P>R

The 3 scenarios where Jim will win this one game of rock, paper, scissors is:

Jim picks Rock, AND Renee picks Scissors. (1/3 * 1/3) = 1/9
Jim picks Scissors, AND Renee picks Paper. (1/3 * 1/3) = 1/9
Jim picks Paper, AND Renee picks Rock. (1/3 * 1/3) = 1/9

The 1st scenario OR the 2nd scenario OR the 3rd scenario will allow Jim to win his one game of rock, paper, scissors. So,

1/9 + 1/9 + 1/9 = 3/9 = 1/3