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# Of the 750 participants in a professional meeting, 450 are female and

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Math Expert
Joined: 02 Sep 2009
Posts: 58402
Of the 750 participants in a professional meeting, 450 are female and  [#permalink]

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24 May 2018, 05:10
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Difficulty:

5% (low)

Question Stats:

93% (01:40) correct 7% (03:01) wrong based on 74 sessions

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Of the 750 participants in a professional meeting, 450 are female and 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) $$\frac{3}{4}$$

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Joined: 07 Dec 2017
Posts: 1140
Re: Of the 750 participants in a professional meeting, 450 are female and  [#permalink]

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24 May 2018, 05:17
Bunuel wrote:
Of the 750 participants in a professional meeting, 450 are female and 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) $$\frac{3}{4}$$

Let's write things out in an organized fashion so we don't get confused.
This is a Precise approach.

750 participants
450 female
1/2 of female = 225 less than 30
1/4 of male = 1/4 of (750 - 450) = 1/4 of 300 = 75 less than 30

So there are a total of 225 + 75 = 300 less than 30.
Then our probability is 300/750 = 30/75 = 10/25 = 2/5

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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2816
Re: Of the 750 participants in a professional meeting, 450 are female and  [#permalink]

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29 May 2018, 16:20
Bunuel wrote:
Of the 750 participants in a professional meeting, 450 are female and 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) $$\frac{3}{4}$$

We see that we have 750 - 450 = 300 males in the meeting. Furthermore, ½(450) = 225 females and ¼(300) = 75 males are less than thirty years old. Therefore, the probability of selecting a person younger than 30 is (225 + 75)/750 = 300/750 = 2/5.

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Intern
Joined: 19 Dec 2018
Posts: 46
Re: Of the 750 participants in a professional meeting, 450 are female and  [#permalink]

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19 Dec 2018, 05:14
Male candidates= 750-450 = 300
½(female candidates)= 225 females candidates < 30 years.
¼(male candidates)=75 males candidates <30 years.
Total candidates less than 30 years= 225+75 = 300candidates.
Probability= 300/750 = 2/5.
Re: Of the 750 participants in a professional meeting, 450 are female and   [#permalink] 19 Dec 2018, 05:14
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