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Of the 750 participants in a professional meeting, 450 are

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Of the 750 participants in a professional meeting, 450 are [#permalink] New post 24 Jan 2017, 02:58
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90% (01:18) correct 9% (01:09) wrong based on 22 sessions


Of the 750 participants in a professional meeting, 450 are female and \(\frac{1}{2}\) of the female and 1/4 of the male participants are less than thirty years old. If one of the participants will be randomly selected to receive a prize, what is the probability that the person selected will be less than thirty years old?

A) \(\frac{1}{8}\)

B) \(\frac{1}{3}\)

C) \(\frac{3}{8}\)

D) \(\frac{2}{5}\)

E) \(\frac{3}{4}\)
[Reveal] Spoiler: OA

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Re: Of the 750 participants in a professional meeting, 450 are [#permalink] New post 28 Jan 2017, 04:27
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Explanation

First, we determine the number of men and woman at the meeting: 750 total – 450 women 300 men

Now we determine the number of each gender under 30:

\(\frac{1}{2}\) of the female participants are less than 30 → \(\frac{1}{2} \times 450\) = 225 women less than thirty

\(\frac{1}{4}\) of the male participants are less than 30 → \(\frac{1}{4} \times 300\) = 75 men less than thirty.

The total number of people less than 30 years of age is 300 (225 + 75).

Finding the probability:

Probability = number of favorable outcomes/number of possible outcomes → \(\frac{300}{750}\) → \(\frac{30}{75}\) → \(\frac{2}{5}\)

Hence option D is correct.
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Re: Of the 750 participants in a professional meeting, 450 are   [#permalink] 28 Jan 2017, 04:27
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Of the 750 participants in a professional meeting, 450 are

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