In a group of 50 persons, 30 like tea, 25 like coffee and 16 like both. How many like
(i) either tea or coffee?
(ii) neither tea nor coffee?
Given:
In a group of 50 persons,
-30 like tea
-25 like coffee
-16 like both tea and coffee
To find:
(i) People who like either tea or coffee.
Let us consider,
Total number of people = n(X) = 50
People who like tea = n(T) = 30
People who like coffee = n(C) = 25
People who like both tea and coffee = n(T ∩ C) = 16
People who like either tea or coffee = n(T ∪ C)
Venn diagram:
Therefore,
n(T ∪ C) = n(T) + n(C) - n(T ∩ C)
= 30 + 25 – 16
= 39
Thus, People who like either tea or coffee = 39
(ii) People who like neither tea nor coffee.
People who like neither tea nor coffee = n(X) – n(T ∪ C)
= 50 – 39
= 11
Therefore, People who like neither tea nor coffee = 11