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

Question

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}

Kinshook · Answer

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

firas92 · Answer

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)

J2S2019 · Answer

IMO correct option is C - Explanation as attachment -

aliakberza · Answer

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.

MahmoudFawzy · Answer

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

shridhar786 · Answer

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

ccheryn · Answer

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

sj24 · Answer

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

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