Two events, A and B, are mutually exclusive if:
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A. B. C. D.B
By definition, if A and B are mutually exclusive, they cannot occur simultaneously. Therefore, P(A and B) = 0 for mutually exclusive events A and B. Note that P(A and B) = P(A).P(B) if and only if A and B are independent. Clearly, if A and B are mutually exclusive, they cannot be independent unless at least one of the two has a zero probability of occurring (i.e. is an impossible event). Finally, the only way "P(A and B) = P(A) + P(B)" will be true is if P(A) = P(B) = 0. To see this, recall that P(A or B) = P(A) + P(B) - P(A and B). The only way for "P(A and B) = P(A) + P(B)" to hold would be to have P(A or B) = 0. This is possible only when P(A) = P
(B) = 0.