UPSC NDA Math Model Paper 5

Let us first calculate the probability of the events A and B from the given data.
P(A)=1−P(ovA)
= 1 − 0.4
= 0.6
Similarly,
P(B)=1−P(B)
= 1 − 0.3
= 0.7
It is already given that P(A ∪ B) = 0.9.
Therefore, the probability of the intersection is given as follows:
P(A ∩ B) = P(A) + P(B) − P(A ∪ B)
= 0.6 + 0.7 − 0.9
= 1.3 − 0.9
= 0.4
Now we will calculate the probability of union of complimentary events as follows:
P(A∪B)=P(A∩B)
= 1 − P(A ∩ B)
= 1 − 0.4
= 0.6
Therefore, the required probability is 0.6.