Which of the following is/are true?
I. If P(A or B) = P(A) + P(B), A and B are independent
II. If P(A and B) = P(A).P(B), A and B are mutually exclusive
III. If P(A and B) = P(A) + P(B), P(A) = P(B) = 0
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A. B. C. D. E.A
If A and B are independent, P(A and B) = P(A).P(B) and vice versa. If A and B are mutually exclusive, P(A and B) = 0. Note that P(A or B) = P(A) + P(B) - P(A and
B). Hence, if P(A and B) = P(A) + P(B), the P(A or B) = 0. This implies that neither A nor B can occur, giving P(A) = P(B) = 0.