Question

I need to know the answer of these questions

Answer 1

(i) The number of people who read at least one of the newspapers.

Answer: 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.