The following Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections. Determine (a) P(A) (b) `P(B nn barC)` (c ) `P(A uu B)` (d) `P(A nn barB)` (e) `P(B nn C)` (f) Probability of the event that exactly one of A, B, and C occurs.

The following Venn diagram shows three events, A, B, and C, and also t

1.	The following Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections. Determine (a) P(A) (b) `P(B nn barC)` (c ) `P(A uu B)` (d) `P(A nn barB)` (e) `P(B nn C)` (f) Probability of the event that exactly one of A, B, and C occurs.
Answer» From the above Venn diagram, (a) `P(A) = 0.13 + 0.07 = 0.20` (b) `P(B nn barC) = P(B) - P(B nn C)` = 0.07 + 0.10 + 0.15 - 0.15 = 0.17 (c ) `P(A uu B) = P(A) + P(B) - P(A nn B)` `= 0.13 + 0.07 + 0.07 + 0.10 + 0.15 - 0.07 = 0.45` (d) `P(A nn barB) = P(A) - P(A nn B) = 0.13 + 0.07 - 0.07 = 0.13` (e) `P(B nn C) = 0//15` (f) P (exactly one of the three occurs) = 0.13 + 0.10 + 0.28 = 0.51

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The following Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections. Determine (a) P(A) (b) `P(B nn barC)` (c ) `P(A uu B)` (d) `P(A nn barB)` (e) `P(B nn C)` (f) Probability of the event that exactly one of A, B, and C occurs.

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