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) \(\frac{29}{32}\)
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Sandy
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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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Sandy
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