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In a class of 60 students, 30 opted for NCC, 32 opted for NSS

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In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that(i) The student opted for NCC or NSS.(ii) The student has opted neither NCC nor NSS.(iii) The student has opted NSS but not NCC.

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In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that(i) The student opted for NCC or NSS.(ii) The student has opted neither NCC nor NSS.(iii) The student has opted NSS but not NCC.

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Text solutionVerified

Solution: Let

A

is the event for selecting

N C

and

B

is the event for selecting

N S S

.
Then,

n (S) = 60, n (A) = 30, n (B) = 32, n (A \cap B) = 24

So,

P (A) = \frac{30}{60} = \frac{1}{2}

P (B) = \frac{32}{60} = \frac{8}{15}

P (A \cap B) = \frac{24}{60} = \frac{2}{5}

(i)Probability that the selected student opted for NCC or NSS,

P (A \cup B) = P (A) + P (B) - P (A \cap B) = \frac{1}{2} + \frac{8}{15} - \frac{2}{5} = \frac{19}{30}

(ii)Probability that the selected student has opted neither NCC nor NSS,

P (A^{'} \cap B^{'}) = 1 - P (A \cup B) = 1 - \frac{19}{30} = \frac{11}{30}

(iii)Probability that the selected student has opted for NSS but not NCC,

P (B - A) = P (B) - P (B \cap A) = \frac{8}{15} - \frac{2}{5} = \frac{2}{15}

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Question Text	In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that(i) The student opted for NCC or NSS.(ii) The student has opted neither NCC nor NSS.(iii) The student has opted NSS but not NCC.
Answer Type	Text solution:1
Upvotes	151

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that(i) The student opted for NCC or NSS.(ii) The student has opted neither NCC nor NSS.(iii) The student has opted NSS but not NCC.

Text solutionVerified

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