Question

in a family 200 families are selected 120 damilies read hindustand time. 100 families reas indian express and 65 fmailies read both the papers. find how many families read at least one newspaper

Answer 1

Answer:

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.

Answer 2

Given:

in a family, 200 families are selected 120 families read Hindustan time. 100 families read Indian express and 65 families read both the papers.

To Find:

find how many families read at least one newspaper

Solution:

We can find the solution to this question by first drawing the Venn diagram for the given situation, A Venn diagram is a graphical representation of sets.

For constructing the Venn diagram we will consider two sets intersecting each other, the value of the intersection will be 65 where it is said that this number is the number of people who read both the papers so the number of people who read,

Only hindustan=120-65

                        =55

Only indian=100-65

                  =35

So the number of families reading at least one newspaper means the family who read only one and both which will be,

=55+65+35

=155

Hence, the number of families reading at least one newspaper is 155.