# 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) = $\inline \dpi{100} \frac{30}{60} = \frac{1}{2}$

P(B) = $\inline \frac{32}{60} = \frac{8}{15}$

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

(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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