### JEE Main 12 Jan 2019 Evening Question 27

##### 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 [JEE Main Online Paper Held On 12-Jan-2019 Evening]

#### Options:

A) $ \frac{1}{6} $

B) $ \frac{5}{6} $

C) $ \frac{1}{3} $

D) $ \frac{2}{3} $

## Show Answer

#### Answer:

Correct Answer: A

#### Solution:

- Let C and S represents the set of students who opted for NCC and NSS respectively.

$ \therefore $ $ n(C)=40,n(S)=30,n(C\cup S)=20 $ Now, $ n(C\cup S)=40+30-20=50 $

So, number of students who has opted neither for NCC nor for NSS are $ 60-50=10 $

So, P(Neither C nor S) $ \frac{10}{60}=\frac{1}{6} $