The joint probability of events A and B is 32 percent with the probability of event A being 60 percent and the probability of event B being 50 percent. Based on this information, the conditional probability of event A given event B has occurred is closest to:
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A. B. C. D.C
To find the conditional probability of event A given event B, we need to use the formula:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both A and B occurring, and P(B) is the probability of event B occurring.
Given that the joint probability of events A and B is 32%, we know that:
P(A and B) = 0.32
Given that the probability of event A is 60% and the probability of event B is 50%, we know that:
P(A) = 0.60 P(B) = 0.50
Plugging these values into the formula, we get:
P(A|B) = P(A and B) / P(B) = 0.32 / 0.50 = 0.64
Therefore, the conditional probability of event A given event B has occurred is 64%, which is closest to answer C.