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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.

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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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