Let P ( A ) = 0.39, P ( B ) = 0.34, and P ( A ? B ) = 0.04. a. Are A and B indep

Question

Let P(A) = 0.39, P(B) = 0.34, and P(A ? B) = 0.04. a. Are A and B independent events? Yes because P(A | B) = P(A). Yes because P(A ? B) ? 0. No because P(A | B) ? P(A). No because P(A ? B) ? 0. b. Are A and B mutually exclusive events? Yes because P(A | B) = P(A). Yes because P(A ? B) ? 0. No because P(A | B) ? P(A). No because P(A ? B) ? 0. c. What is the probability that neither A nor B takes place? (Round your answer to 2 decimal places.)   Probability   
Let P(A) = 0.39, P(B) = 0.34, and P(A ? B) = 0.04.

Explanation / Answer

Two events A and B are independent events if P(A)*P(B)=P(A and B)

here (A and B)=.04   and P(A)*P(B)=.39*.34 =.1326

Thus it is not and independent event

No because P(A and B) is not equal to P(A/B)*P(B)

condition for mutually exclusive P(A and B) should not be equal to 0

here it is not equal to 0 therefore it is not mutually exclusive event option D

P(A or B) = P(A) + P(B) - P(A & B) = .39+.34-.04 = .69

P(neither A nor B) = 1 - P(A or B) = .31

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