CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.45. What is the probability that neither A nor B occurs?
The probability that neither event occurs is 0.25. For mutually exclusive events the probabilities add, so P(A or B) is 0.3 plus 0.45, equal to 0.75, and the complement is 1 minus 0.75, which gives 0.25.
- A0.25Correct
- B0.75
- C0.865
- D0.135
Explanation
Because the events are mutually exclusive, P(A or B) = 0.3 + 0.45 = 0.75. P(neither) = 1 - 0.75 = 0.25. Option 0.135 comes from multiplying the probabilities, which applies to independent events, and 0.75 is the probability of at least one.
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