In a class

Given: Total number of students = 60

So the sample space consist of n(S) = 60

Let A be the event that student opted for NCC and B be the event that the student opted for NSS.

Here being number of students who have opted for both NCC and NSS

(i) P(Student opted for NCC or NSS)

P (A or B) = P(A) + P(B) –P(A and B)

(ii) P(student opted neither NCC nor NSS)

P(not A and not B) =

(by De Morgan’s law)

(iii) P(student opted NSS but not NCC)

n(B - A) = n(B) – n (AB)

⇒ 32 – 24 = 8

The probability that the selected student has opted for NSS and not NCC is