Question

(b) In a group of 140 people, 74 like tea, 104 like milk and each person likes at least one of the two drinks.

How many people like both tea and milk?
(ii) How many people like tea only?
(iii) How many people like milk only?​

Answer 1

How many people like both drinks?

To find the overlap, we can do (104 + 74) - 140 = 38.

How many people like tea only?

To find this, we can do 74 - 38 = 36.

How many people like milk only?

To find this, we can do 104 - 38 = 66.

Answer 2

Explanation:

A = Number of people who likes tea

B = Number of people who likes milk

Total people = n(A U B) = 140

(i) n(AUB) = n(A) + n(B) - n(A ∩B)

n(A∩B) = n(A) + n(B) - n(A ∪B)

n(A∩B) = 74 + 104 - 140

= 178 - 140

n(A∩B) = 38

Number of people who likes both tea and milk = 38

(ii)Number of people who likes tea only = n(A) - n(A∩B)

= 74 - 38

= 36

(iii) Number of people who likes milk only = n(B) -n(A∩B)

= 104 - 38

= 66