Jim and Renee will play one game

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Mon Jan 23, 2012 6:39 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

SOURCE: MGMAT
ANSWER: E

The explination leads the reader to believe this question is so easy - but i still have no idea how to solve this after reading the answer explination. Any explinations are greatly appreciated. Thanks!

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Source: Beat The GMAT — Problem Solving | Mon Jan 23, 2012 6:39 pm

Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Mon Jan 23, 2012 7:41 pm

Here is a detail of all possible scenarios:

If Jim throws a rock here are his out comes depending on Renee's throw:

Renee Rock --> tie
Renee Paper --> Renee Win
Renee Scissor --> Jim Win

If Jim throws a paper here are his out comes depending on Renee's throw:

Renee Rock --> Jim win
Renee Paper --> tie
Renee Scissor --> Renee win

If Jim throws a scissor here are his out comes depending on Renee's throw:

Renee Rock --> Renee tie
Renee Paper --> Jim Win
Renee Scissor --> tie

So, Jim wins 3 of the 9 outcomes or 1/3

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jan 23, 2012 7:41 pm

factor26 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

SOURCE: MGMAT
ANSWER: E

The explination leads the reader to believe this question is so easy - but i still have no idea how to solve this after reading the answer explination. Any explinations are greatly appreciated. Thanks!

Total number of possible combinations = 3 * 3 = 9
There will be a tie when both select Rock or scissors or paper. So, there will be 3 such cases. This means out of the 6 remaining cases, Jim can win 3 times and Renee can win 3 times.
Probability of Jim winning = 3/9 = [spoiler]1/3[/spoiler]

The correct answer is E.

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Mon Jan 23, 2012 7:41 pm

Rock beats Scissors but Scissors don't beat Rock, alternatively with Paper
There are 3C2 ways for these hand signs to show (not 3P2, as we cannot change orders, they only beat the in given way). Hence 3 ways and Jim has opportunity to select 1 out of 3 ways or rephrasing he has 1 chance out of 3 chances to win.

Let's build probability. Renee will start, and his probability that any hand sign shows is 1 or 100% sure he shows some sign. The probability Jill beats Renee's sign is 1 out of 3 and 1* 1/3=1/3

e

factor26 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

SOURCE: MGMAT
ANSWER: E

The explination leads the reader to believe this question is so easy - but i still have no idea how to solve this after reading the answer explination. Any explinations are greatly appreciated. Thanks!

Success doesn't come overnight!

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Mon Jan 23, 2012 7:43 pm

factor26 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

SOURCE: MGMAT
ANSWER: E

The explination leads the reader to believe this question is so easy - but i still have no idea how to solve this after reading the answer explination. Any explinations are greatly appreciated. Thanks!

Each of them has three choices-stone, paper and scissors
So total no of combinations would be 3*3 = 9

Out of the total 9 combinations, Jim can win in three ways :
Jim selects Rock and Renee selects Scissors,
Jim selects Scissors and Renee selects Paper, and
Jim selects Paper and Renee selects Rock

So the probability that Jim will win = 3/9 = 1/3

Option E

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Jan 23, 2012 8:51 pm

Posted an easier solution here
https://www.beatthegmat.com/simple-probl ... tml#442440

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jan 24, 2012 4:21 am

I posted an explanation here:

https://www.beatthegmat.com/simple-probl ... tml#445900

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