Problem Solving

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!

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

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!

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

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

I posted an explanation here:

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