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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:

Options

  1. A7 32
  2. B7 16
  3. C7 64
  4. D3 16

Correct answer

B. 7 16

Step-by-step solution

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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