In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that

(i) The student opted for NCC or NSS.


(ii) The student has opted neither NCC nor NSS.


(iii) The student has opted NSS but not NCC.

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



22