JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Probability

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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) $\frac{1}{6}$ ✓ Correct
(B) $\frac{1}{3}$
(C) $\frac{2}{3}$
(D) $\frac{5}{6}$

Answer: (A)

Solution

By inclusion

-

exclusion the number taking at least one of NCC or NSS is

40 + 30 - 20 = 50

, so

60 - 50 = 10

take neither, and the probability of picking one of those is

\frac{10}{60} = \frac{1}{6}

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option

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