Question

In a class of so students, 35 like to play cricket

Answer 1

Answer:

10

Step-by-step explanation:

Given that:

Total number of students = 50

Students who like to play football = 25

$n(A) = 25$

Students who like to play cricket = 35

$n(B) = 35$

Each student likes to play at least one game.

It means the universal set is equal to the union of the above two sets.

$n(U) =n(A\cup B) = 50$

To find:

The number of students who play both the games and representation of the given situation in the form of a Venn diagram.

i.e. $n(A\cap B) = ?$

Solution:

First of all, let us have a look at the formula for the number of elements in the union of two sets.

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

Putting the values in the formula, we need to find the value of $n(A\cap B)$

$50=25+35-n(A\cap B)\\\Rightarrow 50-60=-n(A\cap B)\\\Rightarrow n(A\cap B)=\bold{10}$

Therefore, the number of students who like to play both the games is 10.