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Question

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T,26 read newspaper I,9 read both H & I,11 read both H & T,8 read both T & I,3 read all three newspapers, then

A
26 People read exactly one newspaper
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B
30 People read exactly one newspaper
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C
19 People read exactly two of the three newspaper
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D
28 People read exactly two of the three newspaper
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Solution

The correct option is C 19 People read exactly two of the three newspaper
Let: H= Set of people who read newspaper H
T= Set of people who read newspaper T
I= Set of people who read newspaper I
n(U)=60;n(H)=25;n(T)=26;
n(I)=26;n(HI)=9;n(HT)=11; and n(TI)=8,n(HTI)=3
Now, let's create a venn diagram for the same and label them as shown:

Now, according to the diagram and the data given we can write:
g=n(HTI)=3
g=3
n(HT)=e+g=11e=8

n(HI)=d+g=9d=6

n(TI)=f+g=8f=5

Now, n(H)=a+e+g+d=25
a+8+3+6=25a=8

n(T)=b+e+g+f=26
b+8+3+5=26b=10

n(I)=c+f+g+d=25
c+5+3+6=26c=12

Now, number of people who read exactly one newspaper =a+b+c=8+10+12=30

Number of people who read exactly two of three newspaper:
=d+e+f=6+8+5=19





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