Question

In a class of $60$ students, $40$ opted for NCC, $30$ opted for NSS and $20$ opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :

• A. $\frac{1}{6}$
• B. $\frac{2}{3}$
• C. $\frac{5}{6}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{1}{6}$

Let $A$ and $B$ be the sets of students who opted for NCC and NSS, respectively.
$n\left(U\right)=60$
$n\left(A\right)=40;n\left(B\right)=30;n(A\cap B)=20$

$n(A\cup B)=40+30-20=50$
$\therefore n(\overline{A}\cap \overline{B})=60-50=10$
Required probability $=\frac{1}{6}$