Question

Question 21 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.

Class X1 - Maths -Probability Page 406

Answer 1

Let A denotes the students of NCC .
B denotes the students of NSS.
total number of students n(S) = 69

Given,
number of students opted for NCC n(A) = 30
number of students opted for NSS n(B) = 32
and number of students opted for both NCC and NSS n( A ∩ B) = 24
so, P(A) = n(A)/n(S) = 30/60
P(B) = n(B)/n(S) = 32/60
P(A ∩ B) = n(A ∩ B)/n(S ) = 24/60
now,
P( students opted for NCC or NSS ) = P(A) + P(B) - P(A∩B)
= 30/60 + 32/60 - 24/60
= (30 + 32 - 24)/60
= 38/60 = 19/30

(ii) P( students opted neither NCC nor NSS) = 1 - P( students opted either NCC or NSS )
= 1 - 19/30
= 11/30

(iii) P( the students opted for NSS but not NCC)
= P( students opted for NCC ) - P( students opted for NCC and NSS )
= 32/60 - 24/60
= 8/60 = 2/15