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Question
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
- The student opted for NCC or NSS.
- The student has opted neither NCC nor NSS.
- The student has opted NSS but not NCC.
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Solution
Let A and B represent the events of opted NCC and NSS respectively.
Total number of students = 60
Number of students who opted for NCC = 30
Probability of being selected for NCC P(A) = `30/60 = 1/2`
Number of students who opted for N.S.S. = 32
∴ Probability of being selected for N.S.S. P(B) = `32/60`
Number of people who opted for NCC and NSS = 24
Probability of opted for NCC and NSS = `24/60`
(i) Probability of being selected for NCC and NSS P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= `30/60 + 32/60 - 24/60`
= `38/60`
= `19/30`
(ii) The probability of not selecting either NCC or NSS
P(A’ ∩ B’) = P[(A ∪ B)’]
= 1 – P(A ∪ B)
= `1 - 19/30`
= `11/30`
(iii) The student has opted for NSS but not NCC
Its probability = P(A’ ∩ B) = P(B) – P(A ∩ B)
= `32/60 - 24/60`
= `8/60`
= `2/15`
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