Question

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis, how many like tennis only and not cricket? How many like tennis?

Answer 1

Let C – Cricket; T – Tennis be the sets. 

Given; n(C’ ∪ T) = 65; n(C) = 40; n(C ∩ T) 

= 10 n(C ∪ T) = n(C) + n(T) – n(C ∩ T) 

⇒ 65 = 40 + n(T) – 10 

⇒ n(T) = 35 n (tennis only and not cricket) 

= n(T ∪ C’) = n(T) – n(T ∩ C) 

= 35 – 10 = 25.