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DS - Probability

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DS - Probability

by karthikpandian19 » Tue Dec 13, 2011 6:36 pm
In a class with 12 children, q of the children are girls. Two children will be randomly chosen simultaneously. What is the value of q?

1) The probability that two girls will be chosen together is 1/11.
2) The probability that one boy will be chosen and one girl will be chosen is 16/33.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Dec 13, 2011 7:54 pm
karthikpandian19 wrote:In a class with 12 children, q of the children are girls. Two children will be randomly chosen simultaneously. What is the value of q?

1) The probability that two girls will be chosen together is 1/11.
2) The probability that one boy will be chosen and one girl will be chosen is 16/33.
(1) Probability that the 1st child will be a girl = q/12
Probability that the 2nd child will be a girl = (q - 1)/(12 - 1) = (q - 1)/11
So, q/12 * (q - 1)/11 = 1/11
q(q - 1) = 12
q² - q - 12 = 0
(q + 3)(q - 4) = 0
q = 4; SUFFICIENT.

(2) # of girls = q, # of boys = 12 - q
Probability that the 1st child will be a girl = q/12
Probability that the 2nd child will be a boy = (12 - q)/(12 - 1) = (12 - q)/11
Similarly, 1st child can be a boy and 2nd be a girl.
So, 2 * q/12 * (12 - q)/11 = 16/33
q(12 - q) = 32
12q - q² = 32
q² - 12q + 32 = 0
(q - 4)(q - 8) = 0
q = 4, 8
No definite answer; NOT sufficient.

The correct answer is A.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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