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Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are mutually exclusive?Select one:a.True.b.false.

Question

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are mutually exclusive?Select one:a.True.b.false.

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Solution

b. False.

The statement is not necessarily true. The conditional probability of A given B is defined as P(A|B) = P(A ∩ B) / P(B). If P(A|B) = 0, it means that the probability of both A and B occurring together is zero. However, this does not necessarily mean that A and B are mutually exclusive.

Mutually exclusive events are events that cannot occur at the same time. In other words, if A happens, B cannot happen and vice versa. This is represented as P(A ∩ B) =

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