UPSC Civil Services 2011 Prelims General Studies Paper II

Given, n (U) = 100
Number of students who play cricket = 60
i.e. n(c) = 60
Number of students who play football = 30
i.e. n (F) = 30
Number of students who play both the games = 10
i.e. n (C ∩ F) = 10
To find : n (C' ∩ F') = ?
we know,
n (C ∪ F) = n (C) + n (F) – n (C ∩ F)
= 60 + 30 –10 = 80
n (C' ∩ F') = n (C ∪ F)' = n (U) – n (C ∪ F)
= 100 – 80
= 20