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

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A class consists of 12 girls and 20 boys. One quarter of the [#permalink]  30 Jul 2018, 10:54
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Question Stats:

75% (00:46) correct 25% (01:28) wrong based on 44 sessions
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) $$\frac{3}{32}$$
(B) $$\frac{9}{32}$$
(C) $$\frac{3}{8}$$
(D) $$\frac{23}{32}$$
(E) $$\frac{29}{32}$$
[Reveal] Spoiler: OA

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Re: A class consists of 12 girls and 20 boys. One quarter of the [#permalink]  31 Jul 2018, 03:01
sandy wrote:
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) $$\frac{3}{32}$$
(B) $$\frac{9}{32}$$
(C) $$\frac{3}{8}$$
(D) $$\frac{23}{32}$$
(E) $$\frac{29}{32}$$

Total : 12 + 20 = 32

Girls who have blue eyes = 12*1/4 = 3

Girls who don't have blue eyes = 9

Probability = 9/32

Retired Moderator
Joined: 07 Jun 2014
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Re: A class consists of 12 girls and 20 boys. One quarter of the [#permalink]  08 Aug 2018, 18:12
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Explanation

The probability of any outcome is equal to the number of desired outcomes divided by the total number of outcomes. There are 12 girls and 20 boys in the classroom. If one-quarter of the girls have blue eyes, then there are $$(12)\frac{1}{3} = 3$$ girls with blue eyes.

Therefore, there are $$12 - 3 = 9$$ girls who do not have blue eyes. The total number of ways in which a child could be chosen is the total number of children in the class, namely 12 + 20 = 32. Therefore, the probability of choosing a girl who does not have blue eyes equals the number of girls without blue eyes divided by the total number of children, which is $$\frac{9}{32}$$.
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Re: A class consists of 12 girls and 20 boys. One quarter of the [#permalink]  10 Aug 2018, 18:11
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sandy wrote:
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) $$\frac{3}{32}$$
(B) $$\frac{9}{32}$$
(C) $$\frac{3}{8}$$
(D) $$\frac{23}{32}$$
(E) $$\frac{29}{32}$$

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 child is a girl who does not have blue eyes is 9/32.

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Re: A class consists of 12 girls and 20 boys. One quarter of the   [#permalink] 10 Aug 2018, 18:11
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