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 news papers. Find: (i) the number of people who read at least one of the newspapers (ii) the number of people who read exactly one newspaper. ‘

Answer 1

Let H = set of people who read paper H. 

I = set of people who read newspaper I 

T = set of people who read newspaper T 

Then, n(H) = 25, n(T) = 26, n(I) = 26, n(H∩I) = 9 

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

(i) Number of people who read at least one newspaper 

n(H∪T∪T) = n(H) + n(T) + n(I) 

-n(H∩T)-n(T∩I)-n(I∩H) + n(H∩T∩I) 

= 25 + 26 + 26-9-11-8 + 3 = 52 

(ii) Number of people who read exactly one paper