UPSC NDA Math Model Paper 2

Let's say that set E is the set of students who passed in English and set H is the set of students who passed in Hindi.
It is given that N = 120, n(E) = 75, n(H) = 50 and n(E ∩ H) = 30.
Number of students who passed in English ONLY:
= n(E) - n(E ∩ H) = 75 - 30 = 45.
Number of students who passed in Hindi ONLY:
= n(H) - n(E ∩ H) = 50 - 30 = 20.
Total number of students who passed in only one subject: n(A) = 45 + 20 = 65.
Required probability =

n(A)

N

=

65

120

=

13

24