In a group of 20 persons, there are 5 graduates. If 3 persons are selected at random from the group, the probability that at least one is graduate is ______.

115/228

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135/228

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225/228

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137/228

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Solution

The correct option is A 137/228
$I n a g r o u p o f 20 p e r s o n$
$n u m b e r o f g r a d u a t e s = 5$
$n u m b e r o f n o n g r a d u a t e s = 15$
$p r o b a b i l i t y o f s e l e c t i n g 3 n o r g r a d u a t e s = \frac{C_{3}^{15}}{C_{3}^{20}} = \frac{273}{684}$
$p r o b a b i l i t y o f a t l e a s t 1 g r a d u a t e = 1 - \frac{273}{684} = \frac{411}{684} = \frac{137}{228}$

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