Events A and B are mutually exclusive. P(A) = 0.45, P(B) = 0.27. The probability of neither A nor B occurring equals ________.
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A. B. C. D.A
The probability of neither A nor B occurring equals one minus the probability of either A or B occurring i.e. P(neither A nor B) = 1 - P(A or B). Now,
P(A or B) = P(A) + P(B) - P(A and B).
Also, for mutually exclusive events, P(A and B) = 0 by definition. Therefore,
P(A or B) = 0.45 + 0.27 = 0.72. Finally, P(neither A nor B) = 1 - P(A or B) = 1 - 0.72 = 0.28.