1

Question

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

Find :

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

(ii) the numbers of people who read exactly one newspaper.

Open in App

Solution

(i) Let

n(P) denote total number of people

n(H) denote number of people who read newspaper H

n(T) denote number of people who read newspaper T and

n(I) denote number of people who read newspaper I

Then, n(P) = 60, n(H) = 25, n(T) = 26, n(I) = 26

n(H∩I)=9,n(H∩T)=11,n(T∩1)=8,n(H∩T∩I)=3

We need to find the number of people who read atleast one of the newspaper, i.e., n(H or T or I), i.e., n(H∪T∪I), i.e., n(H∪T∪I) we know that if A, B, C are 3 sets , then,

n(A∪B∪C)=n(A)+n(B)+n(C)−

n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)

n(H∪T∪I)=n(H)+n(T)+n(I)−

n(H∩T)−n(T∩I)+n(H∩T∩I)

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

= 25+52-28+3

= 25+52-25

=52

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

(ii) Now, we have to calculate the number of people who read exactly one newspaper.

We have,

n(H)+n(T)+n(I)−2n(H∩T)−

2n(T∩I)−2n(H∩I)+3n(H∩T∩I)

= 25+26+26-22-16-18+9= 30

Thus, 30 people can read exactly one newspaper.

94

Join BYJU'S Learning Program

Join BYJU'S Learning Program