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# 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 and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:

(i) the number of people who read at least one of the newspapers

(ii) the number of people who read exactly one newspaper

**Solution:**

Let H be the set of people who read the newspaper H.

T be the set of people who read the newspaper T.

I will be the set of people who read the newspaper I.

It is given that

n (H) = 25, n (T) = 26, n (I) = 26, n (H ∩ T) = 11, n (H ∩ I) = 9, n (T ∩ I) = 8, n (H ∩ T ∩ I) = 3

**(i)** The number of people who read at least one of the newspapers.

We know that

n (H υ T υ I) = n (H) + n (T) + n (I) - n (H ∩ T) - n (H ∩ I) - n (T ∩ I) + n (H ∩ T ∩ I)

= 25 + 26 + 26 - 11 - 9 - 8 + 3

= 80 - 28

= 52

Hence, 52 people read at least one of the newspapers.

(ii) Let x people read newspapers H and T only, y people read newspapers T and I only,

and z people read newspapers H and I

Now, draw the Venn diagram for the given problem.

We can see that,

n ( H ∩ T ∩ I) = a = 3

n ( H ∩ T) = x + a = 11 n (H ∩ I) = z + a = 9 n (T ∩ I) = y + a = 8

Now,

(x + a) + (y + a) + (z + a) = 11 + 8 + 9

x + 3 + y + 3 + z + 3 = 28

x + y + z = 28 - 9

x + y + z = 19

Number of people who read exactly two newspapers = x + y + z = 19

Number of people who read two or more newspapers = 19 + 3 = 22

Therefore,

Number of people who read 3 exactly one newspaper = 52 - 22 = 30

Hence, 30 people read exactly one newspaper

NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 15

## 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 and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find: (i) the number of people who read at least one of the newspapers. (ii) the number of people who read exactly one newspaper.

**Summary:**

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read the newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers is given. We have found that 30 people read exactly one newspaper

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