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

one newspaper (iii) the number of people who read exactly two of three

newspapers. *​

Answer 1

Answer:

Step-by-step explanation:

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

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

Let C be the set of people who read newspaper I.

Given n(A)=25,n(B)=26, and n(C)=26

n(A∩C)=9,n(A∩B)=11, and (B∩C)=8

n(A∩B∩C)=3

Let U be the set of people who took part in the survey.

(i) n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)

=25+26+26−11−8−9+3

=52

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

(ii) Let a be the number of people who read newspapers H and T only.

Let b denote the number of people who read newspapers I and H only.

Let c denote the number of people who read newspaper T and I only.

Let d denote the number of people who read all three newspaper.

Accordingly, d=n(A∩B∩C)=3

Now, n(A∩B)=a+d

n(B∩C)=c+d

n(C∩A)=b+d

∴a+d+c+d+b+d=11+8+9=28

⇒a+b+c+d=28−2d=28−6=22

Hence, (52−22)=30 people read exactly one newspaper.