advita 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?

1/2
1/3
2/3
5/6
5/12

pl explain. thanks.

An age old problem, rather than a real GMAT one. Think holistically: for every sign Jim chooses, he has an equal probability of a win, a lose, or a tie:
If he chooses Rock, then he wins if Renee chooses Scissors (prob = 1/3), loses of she chooses paper (again, prob = 1/3 of that happening), and ties if she also chooses Rock (1/3).
The same if he chooses paper: 1/3 each for win, lose, tie. And the same for scissors.

all in all, Jim as a 1/3 probability of winning, regardless of what he chooses. answer is B.

advita 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?

1/2
1/3
2/3
5/6
5/12

pl explain. thanks.

the probability Jim will select any of the signs out of the set of three signs is equal to the probability Renee will select any of the signs out of the set of three signs OR 1/3

there are three ways how Jim and Renee will select their hand signs for Jim to win, i.e.

Jim S- Renee P
Jim R- Renee S
Jim P- Renee R

equally there are three ways Jim may draw and loose

for descriptive probability chart see the graph below

hence, P(Jim wins)=(1/3*1/3) * 3 = 1/3
P(Jim draws)=(1/3*1/3) * 3 = 1/3
P(Jim looses)=(1/3*1/3) * 3 = 1/3

Geva@MasterGMAT wrote:

advita 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?

1/2
1/3
2/3
5/6
5/12

pl explain. thanks.

An age old problem, rather than a real GMAT one. Think holistically: for every sign Jim chooses, he has an equal probability of a win, a lose, or a tie:
If he chooses Rock, then he wins if Renee chooses Scissors (prob = 1/3), loses of she chooses paper (again, prob = 1/3 of that happening), and ties if she also chooses Rock (1/3).
The same if he chooses paper: 1/3 each for win, lose, tie. And the same for scissors.

all in all, Jim as a 1/3 probability of winning, regardless of what he chooses. answer is B.

I don't get your answer. There are 6 possible outcomes
RS
PR
SP
RR
PP
SS

And there are 3 events out of 6 in wich Jim can win. So I think the answer would be 3/6=1/2

diaca wrote:

Geva@MasterGMAT wrote:

advita 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?

1/2
1/3
2/3
5/6
5/12

pl explain. thanks.

An age old problem, rather than a real GMAT one. Think holistically: for every sign Jim chooses, he has an equal probability of a win, a lose, or a tie:
If he chooses Rock, then he wins if Renee chooses Scissors (prob = 1/3), loses of she chooses paper (again, prob = 1/3 of that happening), and ties if she also chooses Rock (1/3).
The same if he chooses paper: 1/3 each for win, lose, tie. And the same for scissors.

all in all, Jim as a 1/3 probability of winning, regardless of what he chooses. answer is B.

I don't get your answer. There are 6 possible outcomes
RS
PR
SP
RR
PP
SS

And there are 3 events out of 6 in wich Jim can win. So I think the answer would be 3/6=1/2

You forgot to consider these outcomes (which will lead to draw) :
RR
PP
SS

So, now the probability = 3/9 = 1/3

OR

No matter what sign Renee selects, Jim has to select 1 sign to win, 1 sign to draw and 1 sign which will get him loss, so probability of Jim winning is 1/3.

anshumishra wrote:

diaca wrote:

Geva@MasterGMAT wrote:

advita 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?

1/2
1/3
2/3
5/6
5/12

pl explain. thanks.

An age old problem, rather than a real GMAT one. Think holistically: for every sign Jim chooses, he has an equal probability of a win, a lose, or a tie:
If he chooses Rock, then he wins if Renee chooses Scissors (prob = 1/3), loses of she chooses paper (again, prob = 1/3 of that happening), and ties if she also chooses Rock (1/3).
The same if he chooses paper: 1/3 each for win, lose, tie. And the same for scissors.

all in all, Jim as a 1/3 probability of winning, regardless of what he chooses. answer is B.

I don't get your answer. There are 6 possible outcomes
RS
PR
SP
RR
PP
SS

And there are 3 events out of 6 in wich Jim can win. So I think the answer would be 3/6=1/2

You forgot to consider these outcomes (which will lead to draw) :
RR
PP
SS

So, now the probability = 3/9 = 1/3

OR

No matter what sign Renee selects, Jim has to select 1 sign to win, 1 sign to draw and 1 sign which will get him loss, so probability of Jim winning is 1/3.

Im am sorry to insist, but I already took into account those three outcomes. There exist only 6 possible outcomes
RS
PR
SP
RR
PP
SS

RS
RP
RR
PS
PP
PR
SS
SP
SR

These are all the 9 outcomes.

diaca wrote:

anshumishra wrote:

diaca wrote:

Geva@MasterGMAT wrote:

advita 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?

1/2
1/3
2/3
5/6
5/12

pl explain. thanks.

An age old problem, rather than a real GMAT one. Think holistically: for every sign Jim chooses, he has an equal probability of a win, a lose, or a tie:
If he chooses Rock, then he wins if Renee chooses Scissors (prob = 1/3), loses of she chooses paper (again, prob = 1/3 of that happening), and ties if she also chooses Rock (1/3).
The same if he chooses paper: 1/3 each for win, lose, tie. And the same for scissors.

all in all, Jim as a 1/3 probability of winning, regardless of what he chooses. answer is B.

I don't get your answer. There are 6 possible outcomes
RS
PR
SP
RR
PP
SS

And there are 3 events out of 6 in wich Jim can win. So I think the answer would be 3/6=1/2

You forgot to consider these outcomes (which will lead to draw) :
RR
PP
SS

So, now the probability = 3/9 = 1/3

OR

No matter what sign Renee selects, Jim has to select 1 sign to win, 1 sign to draw and 1 sign which will get him loss, so probability of Jim winning is 1/3.

Im am sorry to insist, but I already took into account those three outcomes. There exist only 6 possible outcomes
RS
PR
SP
RR
PP
SS

I already know what my mistake is. It is not the sames SP that PS. So there are nine outcomes
JIM RENEE
R S WIN
R P
R R
S P WIN
S R
S S
P R WIN
P S
P P