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In a class there are 60 boys and 20 girls. Half the boys and girls have merit scholarships. If a student is chosen at random the probability that the student be either a boy or a student with scholarship is

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$\frac{1}{8}$

$\frac{6}{8}$

$\frac{2}{8}$

$\frac{7}{8}$

answer is D.

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Detailed Solution

A=Selected person in a boy

B=Selected person with Scholar Ship

$\begin{array}{rcl} P (A) & = & \frac{60}{80} P (B) = \frac{40}{80} P (A \cap B) = \frac{30}{80} \\ P (A \cup B) & = & \frac{60}{80} + \frac{40}{80} - \frac{30}{80} = \frac{70}{80} = \frac{7}{8} \end{array}$

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