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A class consists of 10 boys and 20 girls. Exactly half of the boys and

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Bunuel
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A class consists of 10 boys and 20 girls. Exactly half of the boys and [#permalink] New post   02 Nov 2020, 08:30
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A class consists of 10 boys and 20 girls. Exactly half of the boys and half of the girls have brown eyes. Determine the probability that a randomly selected student will be a boy or a student with brown eyes.


(A) \(\frac{1}{5}\)

(B) \(\frac{1}{4}\)

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

(D) \(\frac{1}{2}\)

(E) \(\frac{2}{3}\)
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E
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grassbird
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Re: A class consists of 10 boys and 20 girls. Exactly half of the boys and [#permalink] New post   02 Nov 2020, 08:39
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𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)
P(A) = random select a boy = 10/30= 1/3
P(B) = random select a brown eye = half of the class = 15/30=1/2
P( A and B) = boys with brown eyes/entire class = 5/30 = 1/6
1/3 + 1/2 - 1/6 = 2/3
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Re: A class consists of 10 boys and 20 girls. Exactly half of the boys and [#permalink] New post   02 Nov 2020, 17:28
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The main learning here is that a boy is not attached to brown eyes.
Here we have to calculate the probability of selecting a boy, at first, = Number of boys/total students = 10/30= 1/3
A student with brown eyes = (5+10)/30= 1/2
A boy with brown eyes = 5/30= 1/6
SO going with "or" formula = 1/3 + 1/2 -1/6 = 2/3 Answer.
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Re: A class consists of 10 boys and 20 girls. Exactly half of the boys and [#permalink] New post   13 Nov 2020, 08:33
Hi Bunuel,
Thanks for the q. Just thinking why cant we use the logic of (Boys/Total Students) + (Brown eyes / Total Students)? I can feel that something is wrong but can't really separate it out. Pls help!
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Re: A class consists of 10 boys and 20 girls. Exactly half of the boys and [#permalink] New post   16 Nov 2020, 13:20
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Bunuel wrote:
A class consists of 10 boys and 20 girls. Exactly half of the boys and half of the girls have brown eyes. Determine the probability that a randomly selected student will be a boy or a student with brown eyes.


(A) \(\frac{1}{5}\)

(B) \(\frac{1}{4}\)

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

(D) \(\frac{1}{2}\)

(E) \(\frac{2}{3}\)


Solution:

We see that there are 5 brown-eyed boys and 10 brown-eyed girls. The number of students who are boys or have brown eyes is

#(Boys) + #(Brown Eyes) - #(Boys and Brown Eyes)

= 10 + 15 - 5 = 20

Therefore, the desired probability is 20/30 = 2/3.

Answer: E
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Re: A class consists of 10 boys and 20 girls. Exactly half of the boys and [#permalink] New post   16 Nov 2020, 14:21
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UsamaGuddar wrote:
Hi Bunuel,
Thanks for the q. Just thinking why cant we use the logic of (Boys/Total Students) + (Brown eyes / Total Students)? I can feel that something is wrong but can't really separate it out. Pls help!

The problem with this approach is that the boys with brown eyes twice.
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A class consists of 10 boys and 20 girls. Exactly half of the boys and [#permalink] New post   01 May 2023, 01:30
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A class consists of 10 boys and 20 girls. Exactly half of the boys and half of the girls have brown eyes. What is the probability that a randomly selected student will be a boy or a student with brown eyes.

A. 1/3
B. 7/15
C. 8/15
D. 2/3
E. 3/4


This is a PS Butler Question

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Re: A class consists of 10 boys and 20 girls. Exactly half of the boys and [#permalink] New post   01 May 2023, 11:18
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Hi all: Answer is (2/3) or option D.

I followed the double matrix method. with this you will add the total number of boys (10) and the total number of people with Brown eyes (which is 5 for boys and 10 for girls because the prompt says half of each category have brown eyes). therefore 10 + 15 is 25. but you have to subtract the double counting which is 5 boys.

You get 20 total that fit this category. Now divide 20 by 30 and get the answer. voila !
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Re: A class consists of 10 boys and 20 girls. Exactly half of the boys and [#permalink]
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