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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 probability that of events A and B equal to 07 Determine a probability that of events A b probability that of events B and C

Q: 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


(a) P (A)
(b) P\left ( B\cap \bar{C} \right )
(c) P (A ∪ B)
(d) P (A ∩ B)
(e) P (B ∩ C)
(f) Probability of exactly one of the three occurs.

Answers (1)

P (A ∩ B) = 0.07   ……. (given)

  1. P (A) = 0.13 + 0.7 …… (by given Venn diagram)

= 0.20

  1. P (B ∩ \bar{C}) = P (B) – P (B ∩ C)

= 0.07 + 0.10 + 0.15 – 0.15

= 0.07 + 0.10

= 0.17

  1. P (A U B) = P (A) + P (B) – P (A ∩ B) ……. (by general addition rule)

P (A U B) = 0.20 + (0.07 +0.10 +0.15) – 0.07

P (A U B) = 0.20 + 0.25

P (A U B) = 0.45

  1. P (A ∩\bar{B}) = P (A) – P (A ∩ B)

= 0.20 – 0.07

= 0.13

  1. P (B ∩ C) = 0.15     …… (from venn diagram)
  2. P (exactly one of the 3 occurs) = 0.13 + 0.10 + 0.28 = 0.51
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