Question

In a party of 45 people, each one likes tea or coffee or both. 35 people like tea and 20 people like coffee. Find the number of people who 

(i) like both tea and coffee. 

(ii) do not like tea. 

(iii) do not like coffee.

Answer 1

Let the people who like tea be T. 

Let the people who like coffee be C 

By using formula 

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

(i) n(T ∩ C) = n(T) + n(C) – n(T ∪ C) = 35 + 20 – 45 = 55 – 45 = 10 

The number of people who like both coffee and tea = 10.

(ii) The number of people who do not like tea 

n(T) = n(U) – n(T) = 45 – 35 = 10

(iii) The number of people who do not like coffee 

n(C’) = n(U) – n(C) = 45 – 20 = 25.