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A class consists of 12 girls and 20 boys. One quarter of the

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by AAPL » Fri Jan 11, 2019 4:18 am

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Manhattan Prep

A class consists of 12 girls and 20 boys. One-quarter of the girls in the class have blue eyes. If a child is selected at random from the class, what is the probability that the child is a girl who does not have blue eyes?

A. 3/32
B. 9/32
C. 3/8
D. 23/32
E. 29/32

OA B
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by fskilnik@GMATH » Fri Jan 11, 2019 5:47 am
AAPL wrote:Manhattan Prep

A class consists of 12 girls and 20 boys. One-quarter of the girls in the class have blue eyes. If a child is selected at random from the class, what is the probability that the child is a girl who does not have blue eyes?

A. 3/32
B. 9/32
C. 3/8
D. 23/32
E. 29/32
$$? = P\left( {{\rm{girl}}\,{\rm{and}}\,\,{\rm{not}}\,\,{\rm{blue}}} \right)$$
$$20\,{\rm{boys}}\,\,\,{\rm{and}}\,\,\,12\,\,{\rm{girls}}\,\,\,\left\{ \matrix{
\,{1 \over 4}\left( {12} \right) = 3\,\,{\rm{girls}}\,\,{\rm{blue}} \hfill \cr
\,9\,\,\,{\rm{girls}}\,\,{\rm{not}}\,\,{\rm{blue}} \hfill \cr} \right.$$
$$? = {9 \over {12 + 20}} = {9 \over {32}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by [email protected] » Fri Jan 11, 2019 10:07 am
Hi All,

We're told that a class consists of 12 girls and 20 boys. One-quarter of the girls in the class have blue eyes. We're asked for the probability that a randomly selected child is a girl who does NOT have blue eyes. This question comes down to some basic organization and Arithmetic.

From the first sentence, we know that there are 12 girls and 20 boys.

With the second sentence, we can break the 12 girls down into 2 groups: those with blue eyes and those that don't have blue eyes:
(1/4)(12) = 3 with blue eyes
12 - 3 = 9 that don't have blue eyes

The number of girls who DON'T have blue eyes.... out of the total number of students in the class... is 9/32

Final Answer: B

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Rich
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by Scott@TargetTestPrep » Mon Jan 21, 2019 5:33 pm
AAPL wrote:Manhattan Prep

A class consists of 12 girls and 20 boys. One-quarter of the girls in the class have blue eyes. If a child is selected at random from the class, what is the probability that the child is a girl who does not have blue eyes?

A. 3/32
B. 9/32
C. 3/8
D. 23/32
E. 29/32
Since ¼ of the 12 girls have blue eyes, ¼ x 12 = 3 girls have blue eyes. So 9 girls don't have blue eyes.

Since there are 12 + 20 = 32 students in the class, the probability that a randomly selected child is a girl who does not have blue eyes is 9/32.

Answer: B

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