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Given P(A) = 0.6 and P(B) = 0.4, do the following.(a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.1, compute P(A and B).

Question

Given P(A) = 0.6 and P(B) = 0.4, do the following:

(a) If A and B are independent events, compute P(A and B) P(A \text{ and } B) .

(b) If P(AB)=0.1 P(A | B) = 0.1 , compute P(A and B) P(A \text{ 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. This is due to the definition of independence, where the occurrence of one event does not affect the probability of the other event. Therefore, P(A and B) = P(A) * P(B) = 0.6 * 0.4 = 0.24.

(b) If P(A | B) = 0.1, this is the probability of event A given that event B has occurred. By definition, P(A and B) = P(A | B) * P(B). Therefore, P(A and B) = 0.1 * 0.4 = 0.04.

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