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Given P(A) = 0.9 and P(B) = 0.3, do the following.(a) If A and B are independent events, compute P(A and B).(b) If P(A | B) = 0.6, compute P(A and B).

Question

Given P(A) = 0.9 and P(B) = 0.3, do the following.(a) If A and B are independent events, compute P(A and B).(b) If P(A | B) = 0.6, compute P(A and B).

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Solution

(a) If A and B are independent events, the probability of both events occurring is the product of the probabilities of each event. So, P(A and B) = P(A) * P(B) = 0.9 * 0.3 = 0.27.

(b) If P(A | B) = 0.6, this means the probability of event A given that event B has occurred is

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