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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri

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Bunuel
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   25 Jul 2019, 08:00
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

A. \(\frac{3}{20}\)

B. \(\frac{1}{5}\)

C. \(\frac{1}{4}\)

D. \(\frac{3}{10}\)

E. \(\frac{7}{20}\)


 

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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   25 Jul 2019, 08:23
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

A. 3/20

B. 1/5

C. 1/4

D. 3/10

E. 7/20

Please see solution in the image below


IMO C
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   25 Jul 2019, 09:37
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With reference to figure below, the required probability is \(\frac{(X+Y+Z)}{100}\)

Adding up the values from each region, we must get the total of 100

That is,

\((X+Y+Z)+10+25+20+15+5 = 100\)

\((X+Y+Z) = 25\)

Therefore, probability that a member chosen randomly drinks exactly two of the three drinks \(= \frac{25}{100} = \frac{1}{4}\)

Answer is (C)
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   25 Jul 2019, 10:28
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IMO correct option is C - Explanation as attachment -
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   25 Jul 2019, 10:39
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Best way to visualize this problem is to make a pie chart (see attachment).

Now that we have all the data down and its all set up, we can easily deduce that \(x+y+z\) represents the number of people that enjoy exactly two drinks and that: \(25+20+15+10+5+x+y+z=100\) , i.e. only tea + only coffee + only mocha + all three + none + tea & coffee + tea & mocha + mocha & coffee = total group size
==>> \(x+y+z=25\).

So 25 out of a 100 people drink exactly 2 beverages, therefore P(exactly 2 beverages)=\(\frac{25}{100}\) ==>> P(exactly 2 beverages)=\(\frac{1}{4}\).

The answer is C.
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   25 Jul 2019, 17:25
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Total = coffee only + tea only + mocha only + All + none + exactly two
100 = 20+25+15+10+5 + exactly 2
(exactly 2) = 25

so the probability of randomly picking a member who drinks exactly 2 drinks of the 100 people = \(\frac{25}{100} = \frac{1}{4}\)

C
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   25 Jul 2019, 21:10
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total members in the group = 100
members that drink only tea = 25
members that drink only coffee = 20
members that drink only mocha = 15
members that drink all 3 = 10
members that drink none = 5

C is the answer
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   Updated on: 26 Jul 2019, 03:58
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?


Total=only A+pnly B+only C+(sum of EXACTLY 2)+AnBnC+Neither

as per the figure attached total = a + b + c + (d + e +f ) +g + none

here a = 25 who drink only tea
b = 20 who drink only coffee
c = 15 who drink only mocha
g = 10
none =5
(d + e +f ) we have to find given total = 100

substituting


so 25 + 20 + 15 + (sum of EXACTLY 2)+ 10 +5 = 100

(sum of EXACTLY 2) = 25

so the probability of randomly picking EXACTLY 2 is = EXACTLY 2/ members in the group = 25/100 = 1/4
Hence ans C is right
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Originally posted by ccheryn on 25 Jul 2019, 22:01.
Last edited by ccheryn on 26 Jul 2019, 03:58, edited 1 time in total.
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   26 Jul 2019, 01:45
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As shown in the attached picture,

a+b+c = 100-75 = 25 = members who drink exactly two of the three drinks

Probability of them being chosen = 25/100 = 1/4

Ans should be (C)
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink] New post   05 Jul 2022, 03:55
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri [#permalink]
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