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  • Help me answer: 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 :

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 : 

  • Option 1)

    \frac{1}{6}

  • Option 2)

    \frac{2}{3}

  • Option 3)

    \frac{1}{3}

  • Option 4)

    \frac{5}{6}

Answers (1)

best_answer

 

Addition Theorem of Probability -

P\left ( A\cup B \right )= P\left ( A \right )+P\left ( B \right )-P\left ( A\cap B \right )

in general:

P\left ( A_{1}\cup A_{2}\cup A_{3}\cdots A_{n} \right )=\sum_{i=1 }^{n}P\left ( A_{i} \right )-\sum_{i< j}^{n}P\left ( A_{i}\cap A_{j} \right )+\sum_{i< j< k}^{n} P\left ( A_{i}\cap A_{j}\cap A_{k} \right )-\cdots -\left ( -1 \right )^{n-1}P\left ( A_{1}\cap A_{2}\cap A_{3}\cdots \cap A_{n} \right )

-

 

A=NCC

B=NSS

n(A)=40\: \: \: \: \: n(B)=30

n.(A\cup B)=n(A)+n(B)-n(A\cap B)\\\\=30+40-20\\\\=50\\\\P=\frac{60-50}{60}=\frac{1}{6}


Option 1)

\frac{1}{6}

Option 2)

\frac{2}{3}

Option 3)

\frac{1}{3}

Option 4)

\frac{5}{6}

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