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 .

Question

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:

TestHub · Accepted Answer

a = 1 16 c + d + e + f = 1 4 . . . i b + d + e + g = 1 4 . . . . . i i b + f + c + g = 1 4 . . . . i i i Adding i , i i and i i i ⇒ 2 b + c + d + e + f + g = 3 4 ⇒ b + c + d + e + f + g = 3 8 Now ⇒ P A ∪ B ∪ C = a + b + c + d + e + f + g ⇒ P A ∪ B ∪ C = 1 16 + 3 8 ⇒ P A ∪ B ∪ C = 7 16

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