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 neithe

Answer

N/a

Explanation

Let `A=` event that selected student opted for NCC
`B=` event that selected student opted for NSS
Given that total elements in sample, space save,
`n(S)=60`
`n(A)=30,n(B)=32` and `n(AnnB)=24`
`:.P(A)=(n(A))/(n(S))=30/60`
`P(B)=(n(B))/(n(S))=32/60`
and `P(AnnB)=(n(AnnB))/(n(S))=24/60`
(i) Probability that student opted for NCC or NSS
`=P(AuuB)`
`=P(A)+P(B)-P(AnnB)`
`=30/60+32/60-24/60=38/60=19/30`
(ii) Probability that the student has opted neither NCC nor NSS
`=P` (A -not and B-not)
`=P(A'nnB,)=P(AuuB)'`
`=1-P(AuuB)`
`=1-19/30=11/30`
(iii) Probability that the student has opted NSS but nor NCC
`=P(BnnA')=P(B)-P(BnnA)`
`=32/60-34/60`
`=8/60=2/15`