Long Answer TypeTwo students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that:
(a) both Anil and Ashima will not qualify the examination.
(b) at least one of them will qualify the examination.
(c) only one of them will qualfiy the examination.
Short Answer TypeLong Answer TypeIn 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 opted for NSS but not NCC.
Short Answer TypeLong Answer TypeOne number is selected to random from first 100 natural numbers.
n(S) = 100
Event A: The number is divisible by 4.
A = {4, 8, 12, ........, 10} 
n(A) = 25
∴ 
Event B: The number is divisible by 5.
B = {5, 10, 15, ....., 100} 
n(B) = 20
∴ 
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The number is divisible by 4 and 5 i.e., by the l.c.m. 20.
∴ 
∴ 
The events are not mutually exclusive.
∴ P(neither A nor B) = 
= 
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