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It is determined that 25 of every 100 men and 600 of every 1,000 women

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Bunuel
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It is determined that 25 of every 100 men and 600 of every 1,000 women [#permalink] New post   21 Sep 2020, 05:30
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It is determined that 25 of every 100 men and 600 of every 1,000 women wear glasses. If the number of women in a particular room is four times more than that of men, what is the probability of a woman with glasses being randomly selected?

A. 0.47
B. 0.48
C. 0.5
D. 0.52
E. 0.53


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Re: It is determined that 25 of every 100 men and 600 of every 1,000 women [#permalink] New post   21 Sep 2020, 05:51
Probability of men wearing glasses = 25/100 = 0.25
Probability of women wearing glasses = 600/1000 = 0.6

In the room ratio of men to women = 4:1, so probability of choosing a woman randomly = 4/5 = 0.8

Probability of the chosen woman wearing glasses = 0.8 * 0.6 = 0.48. IMO B
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Re: It is determined that 25 of every 100 men and 600 of every 1,000 women [#permalink] New post   21 Sep 2020, 07:04
It is determined that 25 of every 100 men and 600 of every 1,000 women wear glasses. If the number of women in a particular room is four times more than that of men, what is the probability of a woman with glasses being randomly selected?

A. 0.47
B. 0.48
C. 0.5
D. 0.52
E. 0.53

Explanation-

P (Men with glass)=25/100=0.25
P (Women with glass)=600/1000=0.6

given condition, No of Women =4 no. of men
Let say there are 100 men,then there will be 400 women
there will be 25 men with glasses and 400*0.6=240 women with glasses

Now, P (women with glasses)=240/(400+100)
=240/500
=0.48

Hence B is the correct answer.
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Re: It is determined that 25 of every 100 men and 600 of every 1,000 women [#permalink] New post   21 Sep 2020, 10:01
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25 of every 100 men and
600 of every 1,000 women wear glasses.

If the number of women in a particular room is four times more than that of men, W=4M
let us take 400 women and 100 men in a room totaling 500
it has 60*4=240 women and 25 men with glasses

Probability of a woman with glasses being randomly selected=240/500 slightly less than 250/500=1/2~0.48
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Re: It is determined that 25 of every 100 men and 600 of every 1,000 women [#permalink] New post   21 Sep 2020, 10:31
Bunuel wrote:
It is determined that 25 of every 100 men and 600 of every 1,000 women wear glasses. If the number of women in a particular room is four times more than that of men, what is the probability of a woman with glasses being randomly selected?

A. 0.47
B. 0.48
C. 0.5
D. 0.52
E. 0.53


Ratio problems are usually easier if you plug in actual numbers. If there are 100 men and 400 women in a room, then

> 25/100 men wear glasses → 25 of the men wear glasses.
> 60/100 of women wear glasses → 240 of the women wear glasses.

Thus, there are 500 people total and 240 are women who wear glasses. The answer is 240/500 = 0.48.
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Re: It is determined that 25 of every 100 men and 600 of every 1,000 women [#permalink] New post   22 Sep 2020, 01:11
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Probability of men wearing glass: \(\frac{25}{100}\) = 0.25

Probability of women wearing glass: \(\frac{600}{1000}\) = 0.6

The number of women in a particular room is four times more than that of men: Out of every 5 people, there are 4 women and 1 man

Selecting 4 women out of 5 people: \(\frac{4 }{ 5}\)

=>Probability of women out of \(\frac{4 }{ 5}\) who will wear glass: \(\frac{4 }{ 5}\) * 0.6 = 0.48

Answer B
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Re: It is determined that 25 of every 100 men and 600 of every 1,000 women [#permalink] New post   23 Sep 2020, 00:22
Bunuel wrote:
It is determined that 25 of every 100 men and 600 of every 1,000 women wear glasses. If the number of women in a particular room is four times more than that of men, what is the probability of a woman with glasses being randomly selected?

A. 0.47
B. 0.48
C. 0.5
D. 0.52
E. 0.53


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Say number of women in the room is 1000, then number of men is 250.

P(Woman with glasses) = Number of women with glasses/Total number of people in the room = 600/1250 = 0.48
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Re: It is determined that 25 of every 100 men and 600 of every 1,000 women [#permalink]
23 Sep 2020, 00:22
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