21.(i)   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

 (i) The student opted for NCC or NSS.

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.

Given, 

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}

(i) We know,

P(A \cup B) = P(A)+ P(B) - P(A \cap B) 

 \frac{1}{2} + \frac{8}{15} - \frac{2}{5} = \frac{15+16-12}{30}

= \frac{19}{30}

Hence,the probability that the student opted for NCC or NSS is \frac{19}{30}

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