In a group of 50 persons, 30 like tea, 25 like coffee and 16 like both.

Solution:

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 $=n(T \cap C)=16$

People who like either tea or coffee $=n(T \cup C)$

Venn diagram:

Therefore,

$n(T \cup C)=n(T)+n(C)-n(T \cap C)$

$=30+25-16$

$=39$

Thus, People who like either tea or coffee = 39

(ii) People who like neither tea nor coffee.

People who like neither tea nor coffee $=n(X)-n(T \cup C)$

$=50-39$

$=11$

Therefore, People who like neither tea nor coffee = 11