Question

3. In a survey of 50 students of a school, it was found that 30 read newspaper A, 2014
newspaper B and 5 read both the newspapers. Using Venn diagram, find

a. Number of students who read only newspaper A.

b. Number of students who read only newspaper B.

c. Number of students who read none of the newspapers.​

Answer 1

Answer:

We have S=120

i) The number of people who read exactly one newspaper

⇒P(H)+P(T)+P(I)−2((H∩T)+P(T∩I)+P(I∩H))+3P(H∩T∩I)

=50+52+52−2(18+22+16)+3(6)=60

ii) The number of people who read exactly two newspapers

⇒((H∩T)+P(T∩I)+P(I∩H))−3P(H∩T∩I)

=(18+22+16)−3(6)=38

iii) the number of people who read at least one of the newspapers

⇒P(H∪T∪I∪)=P(H)+P(T)+P(I)−((H∩T)+P(T∩I)+P(I∩H))+P(H∩T∩I)

=50+52+52−(18+22+16)+(6)=104