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Jim and Renee will play one game of...

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ameya
 Post subject: Jim and Renee will play one game of...
 Post Posted: Sat May 31, 2008 12:57 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

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.
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Guest
 Post subject:
 Post Posted: Sat May 31, 2008 1:25 pm 
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
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rfernandez
 Post subject:
 Post Posted: Fri Jun 06, 2008 3:49 am 
Offline
ManhattanGMAT Staff


Posts: 386
Answering ameya's question:

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

Rey
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aps_asks
 Post subject: Re: Jim and Renee will play one game of...
 Post Posted: Sun Jan 22, 2012 4:16 am 
Offline
Forum Guests


Posts: 134
Hi instructors ,

Can you confirm that the above answer provided by guest on Sat May 31, 2008 12:25 pm is correct or not ?
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jnelson0612
 Post subject: Re: Jim and Renee will play one game of...
 Post Posted: Sun Jan 22, 2012 11:07 pm 
Offline
ManhattanGMAT Staff


Posts: 1857
aps_asks wrote:
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.

_________________
Jamie Nelson
ManhattanGMAT Instructor
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aps_asks
 Post subject: Re: Jim and Renee will play one game of...
 Post Posted: Thu Jan 26, 2012 8:08 am 
Offline
Forum Guests


Posts: 134
Thanks!
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tim
 Post subject: Re: Jim and Renee will play one game of...
 Post Posted: Thu Feb 02, 2012 7:19 pm 
Offline
ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
:)

_________________
Tim Sanders
Manhattan GMAT Instructor
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