Probability Jim will Win

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getso: Master | Next Rank: 500 Posts; Posts: 141; Joined: Sat Feb 28, 2009 8:19 am; Thanked: 1 times

by getso » Tue Dec 22, 2009 10:20 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

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Source: Beat The GMAT — Problem Solving | Tue Dec 22, 2009 10:20 am

manfromohio: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Dec 22, 2009 10:34 am

by manfromohio » Tue Dec 22, 2009 10:39 am

IMO the answer is 1/3. (E)

Logical explanation: Since both have an equal chance of picking any of the 3, the game is equally likely to favor all possible outcomes - 1/3 Jim Wins, 1/3 Renee wins and 1/3 stalemate (same sign picked by both)

Quant: chance jim wins = Pr.(Jim=Rock) X Pr(Renee=scissors) + Pr.(Jim=Scissors) X Pr(Renee=Paper) +Pr.(Jim=Paper) X Pr(Renee=rock)

= 3 X (1/3)^2
= 3 X 1/9
=1/3.

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mmslf75: Legendary Member; Posts: 503; Joined: Sun Aug 09, 2009 9:53 pmFollowed by: 2 members; Thanked: 31 times

by mmslf75 » Tue Dec 22, 2009 11:56 am

getso wrote: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

This is from MGMAT right ??

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getso: Master | Next Rank: 500 Posts; Posts: 141; Joined: Sat Feb 28, 2009 8:19 am; Thanked: 1 times

by getso » Tue Dec 22, 2009 8:10 pm

Yes it is from MGMAT.

@Manfromohio: Thanks for the explanation.

OA is
[spoiler]1/3[/spoiler]

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viidyasagar: Community Manager; Posts: 156; Joined: Mon Oct 22, 2007 6:06 amFollowed by: 3 members; Location: Mumbai, India; Thanked: 16 times; GMAT Score:700

by viidyasagar » Fri Dec 25, 2009 2:53 am

Correct me if i am wrong.....

I dont care what jim picks....i only care what Renee picks after Jim picks a sign......coz either of the 3 picks could result in a win for Jim.....

Hence the answer is (3/3)*(1/3).....jim can choose to pick any of the 3 signs...hence 3 out of 3.....given that jim has picked a sign, renee can pick only 1 of the three signs so that Jim wins....Renee's probability is 1 out of 3..... and the answer too IMO is 1/3

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