For three events A, B, and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = 1/4 and P(All the three events occur simultaneously) = 1/16. Then the probability that at least one of the events occurs, is?

P(exactly one of A or B) = P(A∪B) − P(A∩B) = 1/4 = P(A) + P(B) − P(A∩B)
P(exactly one of C or B) = P(C∪B) − P(C∩B) = 1/4 = P(C) + P(B) − P(C∩B)
P(exactly one of A or C) = P(A∪C) − P(A∩C) = 1/4 = P(A) + P(C) − P(A∩C)
Adding all:
2P(A) + 2P(B) + 2P(C) − P(A∩B) − P(A∩C) − P(B∩C) = 3/4
P(A) + P(B) + P(C) − P(A∩B) − P(A∩C) − P(B∩C) = 3/8
P(A∪B∪C) = P(A) + P(B) + P(C) − P(A∩B) − P(A∩C) − P(B∩C) + P(A∩B∩C) = 3/8 + 1/16 = 7/16