Answer is (A) 7/16
We have P(Exactly one of A or B occurs) = P(A) + P(B) − 2P (A ∩ B) = 1/4
P(Exactly one of B or C occurs) = P(B) + P(C) - 2P(B ∩ C) = 1/4
P(Exactly one of C or A occurs) = P(C) + P(A) - 2P(C ∩ A) = 1/4
Adding all, we get
Now, it is given that all the three events occur simultaneously, which is given by
P(A ∩ B ∩ C = 1/16
Therefore, the probability that at least one of the events occurs, is