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The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance,

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The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P (A ∩ B) = .07. Determine (f) Probability of exactly one of the three occurs. Select the correct answer from above options

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Given P(A ⋂ B) = 0.07 From the given Venn Diagram (a) P(A) = 0.07 + 0.10 + 0.15 – 0.15 = 0.07 + 0.10 = 0.17 (c) P(A ⋃ B) By General Addition Rule, P(A ⋃ B) = P(A) + P(B) – P(A ⋂ B) ⇒ P(A ⋃ B) = 0.20 + (0.07 + 0.10 + 0.15) – 0.07 ⇒ P(A ⋃ B) = 0.20 + 0.25 ⇒ P(A ⋃ B) = 0.45 = 0.20 – 0.07 [from part (a)] = 0.13 (e) P(B ⋂ C) P(B ⋂ C) = 0.15 (f) Probability of exactly one of the three occurs P(exactly one of the three occurs) = 0.13 + 0.10 + 0.28 = 0.51

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