A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
a) 1/126
b) 1/120
c) 1/24
d) 4/25
e) 1/2
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Probability - 10 marbles
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Brent@GMATPrepNow
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Last edited by Brent@GMATPrepNow on Fri Jun 15, 2012 9:48 am, edited 2 times in total.
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Brent@GMATPrepNow
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Nope, it's not C - keep at itMr2Bits wrote:5/5! = 5/120 = 1/24
= C
Brent Hanneson - Creator of GMATPrepNow.com
if all girls have the same colour, they will either have all white or all black marbles. this is only possible in 2 outcomes
The total number of outcomes is 10!
But since we have only 2 different elements it should be divided by 5! 5!
10! / (5! 5!) = 252
so the answer is
2/252 = 1/126 (A) ???
I am not sure about my logic, but it fits to one of your answer choices
The total number of outcomes is 10!
But since we have only 2 different elements it should be divided by 5! 5!
10! / (5! 5!) = 252
so the answer is
2/252 = 1/126 (A) ???
I am not sure about my logic, but it fits to one of your answer choices
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Brent@GMATPrepNow
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The answer is, indeed, A (1/126)
Here's my solution:
The easiest/fastest way to determine the probability is to examine the probability of each necessary outcome to guarantee that the girls (and subsequently the boys) draw the same colored marble.
We get [P(1st girl selects any marble) x P(2nd girl selects marble the same color as 1st girl) x P(3nd girl selects marble the same color as 1st girl) x P(4th girl selects marble the same color as 1st girl) x P(5th girl selects marble the same color as 1st girl) x P(boys getting same color ball from remaining balls)
This equals: 1 x 4/9 x 3/8 x 2/7 x 1/6 x 1
Which equals: 1/126
Here's my solution:
The easiest/fastest way to determine the probability is to examine the probability of each necessary outcome to guarantee that the girls (and subsequently the boys) draw the same colored marble.
We get [P(1st girl selects any marble) x P(2nd girl selects marble the same color as 1st girl) x P(3nd girl selects marble the same color as 1st girl) x P(4th girl selects marble the same color as 1st girl) x P(5th girl selects marble the same color as 1st girl) x P(boys getting same color ball from remaining balls)
This equals: 1 x 4/9 x 3/8 x 2/7 x 1/6 x 1
Which equals: 1/126
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720dreaming
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I got A, 1/126. Here is my logic.
First girl picks a marble. Prob 1.
Second girl must pick the same color marble. Prob (4/9)
Third girl must pick the same color marble. Prob (3/8)
Fourth girl must pick the same color marble. Prob (2/7)
Fifth girl must pick the same color marble. Prob (1/6)
So....
1*(4/9)*(3/8)*(2/7)*(1/6)=1/126
First girl picks a marble. Prob 1.
Second girl must pick the same color marble. Prob (4/9)
Third girl must pick the same color marble. Prob (3/8)
Fourth girl must pick the same color marble. Prob (2/7)
Fifth girl must pick the same color marble. Prob (1/6)
So....
1*(4/9)*(3/8)*(2/7)*(1/6)=1/126
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logitech
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Let me take over from heremoshum wrote:if all girls have the same colour, they will either have all white or all black marbles. this is only possible in 2 outcomes
The total number of outcomes is 10!
But since we have only 2 different elements it should be divided by 5! 5!
10! / (5! 5!) = 252
Than we want either WWWWWBBBBB or BBBBBWWWWW
so out of 252 combinations we only need two of them
2/252 will do the magic for us in this question.
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bluementor
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I don't get it. Why do you assume that all the girls will pick the marbles first before the boys do or vice versa? If the girls and boys picked a marble each in turns, the result would be different.720dreaming wrote:I got A, 1/126. Here is my logic.
First girl picks a marble. Prob 1.
Second girl must pick the same color marble. Prob (4/9)
Third girl must pick the same color marble. Prob (3/8)
Fourth girl must pick the same color marble. Prob (2/7)
Fifth girl must pick the same color marble. Prob (1/6)
So....
1*(4/9)*(3/8)*(2/7)*(1/6)=1/126
The probability of a second girl to picking the same color marble can be any of the following:
1. 4/9 : if she is the 2nd person picking a marble
2. 4/8: if she is the 3rd person picking a marble (i.e. the first boy picks before her)
3. 4/7: if 2 boys pick marbles before the 2nd girl
...and so on, and a similar logic for the 3rd, 4th and 5th girl.
Could anyone please explain? Thanks.
-BM-
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Ian Stewart
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You're free to assume the boys and girls pick the marbles in any order you find convenient (or if you like, you can assume they all pick marbles simultaneously). Provided you do the math right, the answer will be the same in every case, which should make intuitive sense. If the boys and girls alternate, as in your scenario above, you could calculate the result as follows:bluementor wrote:I don't get it. Why do you assume that all the girls will pick the marbles first before the boys do or vice versa? If the girls and boys picked a marble each in turns, the result would be different.720dreaming wrote:I got A, 1/126. Here is my logic.
First girl picks a marble. Prob 1.
Second girl must pick the same color marble. Prob (4/9)
Third girl must pick the same color marble. Prob (3/8)
Fourth girl must pick the same color marble. Prob (2/7)
Fifth girl must pick the same color marble. Prob (1/6)
So....
1*(4/9)*(3/8)*(2/7)*(1/6)=1/126
The probability of a second girl to picking the same color marble can be any of the following:
1. 4/9 : if she is the 2nd person picking a marble
2. 4/8: if she is the 3rd person picking a marble (i.e. the first boy picks before her)
3. 4/7: if 2 boys pick marbles before the 2nd girl
...and so on, and a similar logic for the 3rd, 4th and 5th girl.
Could anyone please explain? Thanks.
-BM-
1st (girl): can pick any marble
2nd (boy): must pick the colour the first girl did not pick: 5/9
3rd (girl): must pick same as the first girl: 4/8
4th (boy): must pick same as the first boy: 4/7
5th (girl): must pick same as other girls: 3/6
and so on. Multiplying these, you get:
(5/9)*(4/8)*(4/7)*(3/6)*(3/5)*(2/4)*(2/3)*(1/2)
= (5*4*4*3*3*2*2)/9!
= (4*3*2)/(9*8*7*6)
= 1/(3*7*6)
= 1/126
I'd find this approach a lot less convenient then the approaches suggested above, but there's no reason why it shouldn't give you the same answer.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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neerajkumar1_1
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I thought of it in a different way...
essentially the answer will be the same...
There will be two required combinations...
WWWWWBBBBB or BBBBBWWWWW
i suppose the key is that one should realize that the prob of boys picking up the ball is 1...
so prob = 5/10 * 4/9 * 3/8 * 2/7 * 1/6 * 2
= 1/126
Pick A
essentially the answer will be the same...
There will be two required combinations...
WWWWWBBBBB or BBBBBWWWWW
i suppose the key is that one should realize that the prob of boys picking up the ball is 1...
so prob = 5/10 * 4/9 * 3/8 * 2/7 * 1/6 * 2
= 1/126
Pick A
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mvikred
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5!x5!x2
---------
10!
= 1/126
therefore, the answer is A
since everyone has a different approach above, let me explain my approach.
if all the girls were to choose black, then black marbles can be distributed in 5! ways ... and the remaining white marbles are distributed among the guys in 5! ways .. since the girls can chose either black or white .. the total number of ways in which all the girls end up having the same colored marbles is 5!.5!.2
total number of ways in which all the children pick the marbles is 10!
therefore the probability is = 5!.5!.2 / 10! = 1/126
NOTE: I believe if the marbles are identical then the answer would be different (please correct me if i am wrong)
---------
10!
= 1/126
therefore, the answer is A
since everyone has a different approach above, let me explain my approach.
if all the girls were to choose black, then black marbles can be distributed in 5! ways ... and the remaining white marbles are distributed among the guys in 5! ways .. since the girls can chose either black or white .. the total number of ways in which all the girls end up having the same colored marbles is 5!.5!.2
total number of ways in which all the children pick the marbles is 10!
therefore the probability is = 5!.5!.2 / 10! = 1/126
NOTE: I believe if the marbles are identical then the answer would be different (please correct me if i am wrong)
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mundasingh123
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Hi Brent .Thanks for the awesome questionBrent Hanneson wrote:Source: Beat The GMAT Practice Questions
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
a) 1/126
b) 1/120
c) 1/24
d) 4/25
e) 1/2
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nipunkathuria
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i also got answer as A 1/126, with the following approach.
P(1st girl getting Blue Marble)xP(2nd girl getting Blue Marble)xP(3rd girl getting Blue Marble)xP(4th girl getting Blue Marble)xP(5th girl getting Blue Marble)=5/10x4/9x3/8/x2/7x1/6
the same probability will exist for all the girls to pick up black marbles, so final probability will be
2x(5/10x4/9x3/8/x2/7x1/6)=1/126
P(1st girl getting Blue Marble)xP(2nd girl getting Blue Marble)xP(3rd girl getting Blue Marble)xP(4th girl getting Blue Marble)xP(5th girl getting Blue Marble)=5/10x4/9x3/8/x2/7x1/6
the same probability will exist for all the girls to pick up black marbles, so final probability will be
2x(5/10x4/9x3/8/x2/7x1/6)=1/126
