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Probability question

2019 · 12 Jan · Shift 2 · Q39
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  5. /2019 · 12 Jan · Shift 2 · Q39

Probability question

2019 · 12 Jan · Shift 2 · Q39

JEE MainMathematicsProbabilityMCQ+4 / −1
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 students selected has opted neither for NCC nor for NSS is :
  1. A
    13{1 \over 3}31​
  2. B
    16{1 \over 6}61​
  3. C
    23{2 \over 3}32​
  4. D
    56{5 \over 6}65​
View written solutionFree

Correct answer: B

  1. Let:

    • NNN = students who opted for NCC
    • SSS = students who opted for NSS

    Given:

    \quad n(N)=40, \quad n(S)=30, \quad n(N\cap S)=20$$

  2. Find the number of students who opted for at least one of NCC or NSS using inclusion-exclusion: n(N∪S)=n(N)+n(S)−n(N∩S)n(N\cup S)=n(N)+n(S)-n(N\cap S)n(N∪S)=n(N)+n(S)−n(N∩S) n(N∪S)=40+30−20=50n(N\cup S)=40+30-20=50n(N∪S)=40+30−20=50

  3. Therefore, the number of students who opted for neither NCC nor NSS is: 60−50=1060-50=1060−50=10

  4. Hence the required probability is: 1060=16\frac{10}{60}=\frac{1}{6}6010​=61​

  5. Check options:

    • A: 13\frac{1}{3}31​ ❌
    • B: 16\frac{1}{6}61​ ✅
    • C: 23\frac{2}{3}32​ ❌
    • D: 56\frac{5}{6}65​ ❌

So, the correct option is B.

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