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by nahid078 » Sat Sep 05, 2015 8:12 pm
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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by Brent@GMATPrepNow » Sat Sep 05, 2015 8:40 pm
nahid078 wrote: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
There's a VERY long thread about this question here: https://www.beatthegmat.com/probability- ... 28296.html

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.

So, P(all girls select same color) = P(1st girl selects any marble AND 2nd girl selects marble the SAME color as 1st girl AND 3rd girl selects marble the SAME colorAND 4th girl selects marble the SAME colorAND 5th girl selects marble the SAME color AND the boys get the rest)
= 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(the boys get the rest)

This equals: 1 x 4/9 x 3/8 x 2/7 x 1/6 x 1
= [spoiler]1/126[/spoiler]
= A

NOTE: The 1 at the beginning of the product represents the probability that the 1st girls selects any marble. Since this first girl can select any marble, the probability is 1 that she will accomplish this.

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Brent
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by Max@Math Revolution » Sun Sep 06, 2015 5:43 am
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


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

The number of all cases 5 girls choose 5 marbles among 10 marbles are 10C5.
Moreover the number of cases 5 girls choose all white marbles 5C5.
So the probability 5 girls choose 5 white marbles 5C5 / 10C5 = 1/252.
Similarly the probability 5 girls choose 5 black marbles 5C5 / 10C5 = 1/252.
So the answer is 2* 1/252 = 1/126. (a)



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