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, II 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.

Answer 1

Let H=H= set of people who read paper HH
I=I= set of people who read newspaper II
T=T= set of people who read newspaper TT
then n(H)=25,n(T)=26,n(I)=26,n(H∩I)=9n(H)=25,n(T)=26,n(I)=26,n(H∩I)=9
n(H∩T)=11,n(T∩I)=8,n(H∩T∩I)=3n(H∩T)=11,n(T∩I)=8,n(H∩T∩I)=3
Number of people who read atleast on newspaper
n(H∪T∪T)=n(H)+n(T)+n(I)n(H∪T∪T)=n(H)+n(T)+n(I)
−n(H∩T)−n(T∩I)−n(I∩H)+n(H∩T∩I)−n(H∩T)−n(T∩I)−n(I∩H)+n(H∩T∩I)
=25+26+26−9−11−8+3=52