UPSC NDA Math Model Paper 6

Given: The Probability of at least one of the events A and B occurs = P(A ∪ B) = 0.6
The probability that A and B occur simultaneously = P(A ∩ B) = 0.2
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
0.6 = P(A) + P(B) - 0.2
P(A) + P(B) = 0.8
P(A)’ = 1 - P(A) ----(1)
P(B)’ = 1 - P(B) ----(2)
Adding (1) & (2)
P(A)’ + P(B’) = 2 - [P(A) + P(B)]
= 2 - [0.8]
= 2 - 0.8
= 1.2