Question 7: In a class of 55 students, 34 like to play cricket and 30 like to play hockey. Also each student likes to play at least one of the two games. How many students like to play both games?
Solution:
Let \(C=\text{Students who like cricket}\; ;\) \(\;H=\text{Students who like hockey}\)
We are given
\(n(C)=34\;\)
\(n(H)=30\;\)
\(n(C\cup H)=55\;\) (Since every student likes at least one)
\(n(C\cap H)=?\;\) (students who like both)
We know that
\(n(C\cup H)=n(C)+n(H)−n(C\cap H)\)
\(55=34+30-n(C\cup H)\)
\(n(C\cap H)=34+30-55\)
\(n(C\cap H)=9\)
\(\boxed{9 \text{ students like both games}}\)