In a class of 60 students ,30 opted for NCC, 32 opted for NSS and 24 opted for both NSS and NCC.Find the number of students opted
a) only NCC b) NCC OR NSS c) neither NCC nor NSS
Answers
Answer:
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
Given, number of students who have opted for NCC i.e. n(A)=30
∴P(A)=
60
30
=
2
1
Also, given number of students who have opted for NSS i.e. n(B)=32
∴P(B)=
60
32
=
15
8
Also, given number of students who have opted for both NCC and NSS i.e. n(A∩B)=24
∴P(A∩B)=
60
24
=
5
2
(i) We know that P(A∪B)=P(A)+P(B)−P(A∩B)
∴P(A∪B)=
2
1
+
15
8
−
5
2
=
30
15+16−12
=
30
19
Thus the probability that the selected student has opted for NCC or NSS is
30
19
(ii) P(not A and not B)
= P(A' and B')
= P(A
′
∩B
′
)
= P(A∪B)
′
[(A
′
∩B
′
)=(A∪B)
′
(by De Morgan's law)]
=1−P(A∪B)
=1−P(AorB)
=1−
30
19
=
30
11
Thus the probability that the selected students has neither opted for NCC nor NSS is
30
11
(iii) Number of students who have opted for NSS but not NCC
=n(B−A)=n(B)−n(A∩B)
=32−24=8
So, the probability that the student has opted for NSS but not NCC is
60
8
=
15
2
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Answer:
a) 30
b) 62
c) 24
THESE ARE THE CORRECT ANSWERS