The probability that events A and B do not occur simultaneously equals 0.77. The probability of neither A nor B occurring equals 0.38. If P(A) equals 0.26, the probability of B occurring equals ________.
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A. B. C. D.Explanation
The probability that events A and B do not occur simultaneously equals one minus the probability that events A and B occur simultaneously. Thus,
P(A and B) = 1 - 0.77 = 0.23.
The probability of neither A nor B occurring equals one minus the probability of either A or B occurring. Thus, P(A or B) = 1 - 0.38 = 0.62.
Now, P(A or B) = P(A) + P(B) - P(A and B). Therefore, P(B) = P(A or B) - P(A) + P(A and B) = 0.62 - 0.26 + 0.23 = 0.59.