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 be the set of people who like cricket and T be the set of people who like tennis.

Here $n\left(C\right)=40,n(C\cap T)=10$ and $n(C\cup T)=65.$

We know that

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

$\therefore$ $65=40+n\left(T\right)-10$

$\therefore$ $n\left(T\right)=65-30=35$

$\therefore$ Number of people who like tennis = 35

Now number of people who like tennis only and not cricket

$=n(T-C)$

$=n\left(T\right)-n(C\cap T)$

$=35-10=25.$