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:

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 at least one of the newspapers.
(ii) the number of people who read exactly one newspaper.
Answer
(i) the number of people who read at least one of the newspapers.
Let H,T and I be the set of people who read newspaper H, T and C respectively.
n(H) = 25, n(T) = 26,n(I) = 26, n(H ∩ I) = 9, n(H ∩ T) = 11, n(T ∩ I) = 8 and n(H ∩ T ∩ I) = 3
Use formula
n(H ∪ T ∪ I) = n(H) + n(T) + n(I) - n(H ∩ T) - n(T ∩ I) - n(I ∩ H) + n(H ∩ T ∩ I)
Plug the values we get
= 25 + 26 + 26 - 11 - 8 - 9 + 3
= 52
The number of people who read at least one of the newspapers = n(H ∪ T ∪ I) = 52
(ii)The number of people who read exactly one newspaper
= n(H ∪ T ∪ I) - n(H ∩ T) - n(T ∩ I) - n(I ∩ H) + 2 × n(H ∩ T ∩ I)
Plug the values we get
= 52 -11 -8 -9 + 2× 3
= 52 -28 + 6
= 58 – 28
= 30
Hence, 30 people read exactly one newspaper.