Test the pair of events B and E for independence based on the following table. A B C Total D 0.25 0.05 0.30 0.60 E 0.04 0.09 0.07 0.20 F 0.01 0.06 0.13 0.20 Total 0.30 0.20 0.50 1.00 Are B and E independent or dependent and why? Select the correct answer below and fill in the answer boxes to complete your choice. A. B and E are independent because $P(B \cap E)$ does not equal $P(B)P(E)$. $P(B \cap E) = $ and $P(B)P(E) = $ B. B and E are independent because $P(B \cap E)$ equals $P(B)P(E)$. $P(B \cap E) = $ and $P(B)P(E) = $ C. B and E are dependent because $P(B \cap E)$ does not equal $P(B)P(E)$. $P(B \cap E) = $ and $P(B)P(E) = $ D. B and E are dependent because $P(B \cap E)$ equals $P(B)P(E)$. $P(B \cap E) = $ and $P(B)P(E) = $
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Test the pair of events D and E for independence based on the following table. Events A, B, and C are mutually exclusive. Events D and E are mutually exclusive. Are the events D and E independent? Select the correct answer below and fill in the answer boxes to complete your choice. A. Yes, they are independent because P(D∩E) = P(D)P(E). P(D∩E) = and P(D)P(E) = B. No, they are not independent P(D∩E) = P(D)P(E). P(D∩E) = and P(D)P(E) = C. No, they are not independent because P(D∩E) ≠ P(D)P(E). P(D∩E) = and P(D)P(E) = D. Yes, they are independent because P(D∩E) ≠ P(D)P(E). P(D∩E) = and P(D)P(E) =
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Test the pair of events E and D for independence based on the following table. Events A, B, and C are mutually exclusive. Events D and E are mutually exclusive. Are the events E and D independent? Select the correct answer below and fill in the answer boxes to complete your choice. A. No, they are not independent because P(E∩D) ≠ P(E)P(D). P(E∩D) = and P(E)P(D) = . B. Yes, they are independent because P(E∩D) ≠ P(E)P(D). P(E∩D) = and P(E)P(D) = . C. No, they are not independent P(E∩D) = P(E)P(D). P(E∩D) = and P(E)P(D) = . D. Yes, they are independent because P(E∩D) = P(E)P(D). P(E∩D) = and P(E)P(D) = .
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Use the Test for Independence to determine if events A and B are independent. P(A) = 0.4, P(B) = 0.3, P(A ∩ B) = 0.12. Select the correct choice below and fill in the answer boxes to complete your choice (Type an integer or a decimal.) A. Events A and B are not independent because P(A ∩ B) and P(A ∩ B) = 0. B. Events A and B are not independent because P(A ∩ B) = 0.12 and P(A)P(B) = 0.12. C. Events A and B are independent because P(A ∩ B) = 0.12 and P(A)P(B). D. Events A and B are independent because P(A ∩ B) and P(A) + P(B) - P(A ∩ B).
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