Question -
Answer -
From the question it is given that,
The total number of students in class = 60
Thus, the sample space consist of n(S) = 60
Let us assume that the students opted for NCC be тАШAтАЩ
And also assume that the students opted for NSS be тАШBтАЩ
So, n(A) = 30, n(B) = 32 , n(AтИйB) = 24
We know that, P(A) = n(A)/n(S)
= 30/60
= ┬╜
P(B) = n(B)/n(S)
= 32/60
= 8/15
P(AтИйB) = n(AтИйB)/n(S)
= 24/60
= 2/5
Therefore, P(AтИкB)= P(A) + P(B) тАУ P(AтИйB)
(i) The student opted for NCC or NSS.
P (A or B) = P(A) + P(B) тАУP(A and B)
P(AтИкB) = P(A) + P(B) тАУ P(AтИйB)
= ┬╜ + (8/15) тАУ (2/5)
= 19/30
(ii)┬аP(student opted neither NCC nor NSS)
P(not A and not B) =┬аP(AIтИйBI)
We know that, P(AIтИйBI) = 1 тАУ P(AтИкB)
= 1 тАУ (19/30)
= 11/30
(iii)┬аP(student opted NSS but not NCC)
n(B тАУ A) = n(B) тАУ n (AтИйB)
тЗТ┬а32 тАУ 24 = 8
The probability that the selected student has opted for NSSand not NCC is
= (8/60) = 2/15