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

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

Answers (1)
H Harsh Kankaria

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


n(S) = 60, n(A) = 30, n(B) =32, n(A \cap B) = 24

Therefore, P(A) = \frac{30}{60} = \frac{1}{2}

P(B) = \frac{32}{60} = \frac{8}{15}

P(A \cap B) = \frac{24}{60} = \frac{2}{5}

(iii) Now,

Probability that the student has opted NSS but not NCC = P(B \cap A' ) = P(B-A)

We know,

P(B-A) = P(B) -  P(A \cap B) 

= \frac{8}{15}- \frac{2}{5} = \frac{8-6}{15}

= \frac{2}{15}

Hence,the probability that the student has opted NSS but not NCC is \frac{2}{15}