Question

Example \( 8.31 \) In a class of 50 students, 28 opted for NCC, 30 opted for NSS and 18 opted both NCC and NSS. One of the students is selected at random. Find the probability that (i) The student opted for NCC but not NSS.

Answer 1

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

∴ n(A) = 28, n(B) = 30 and n(A ∩ B) = 18

∵ There are 50 students in class.

∴ n(U) = 50

Now, number of students which opted for NCC but not NSS is n(A only) = n(A) - n(A ∩ B)

= 28-18

= 10

∴ Probability = P(A only) \(=\frac{n(A\,only)}{n(U)}\)

= 10/50 = 1/5

Hence, probability that students opted for NCC but not NSS be 1/5.