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Asked by Shruthi Last Modified
Answer 
Nurullmobeen
Let A be the event in which the selected student has opted for NCC and B be the event in which the selected student has opted for NSS.
Total number of students = 60
Number of students who have opted for NCC = 30
∴ P(A) =
Number of students who have opted for NSS = 32
Number of students who have opted for both NCC and NSS = 24
(i) We know that P(A or B) = P(A) + P(B) – P(A and B)
Thus, the probability that the selected student has opted for NCC or NSS is
.
(ii)
Thus, the probability that the selected students has neither opted for NCC nor NSS is
.
(iii) The given information can be represented by a Venn diagram as
It is clear that
Number of students who have opted for NSS but not NCC
= n(B – A) = n(B) – n(A ∩ B) = 32 – 24 = 8
Thus, the probability that the selected student has opted for NSS but not for NCC = 
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