FRM Part I · FRM Exam Part I · Fundamentals of Probability
For a bond portfolio, P(A) = 0.30 is the probability that interest rates rise and P(B) = 0.45 is the probability that credit spreads widen. The probability that at least one of these occurs is 0.60. What is the probability that both occur?
The probability that both events occur is 0.15. Using the addition rule, P(A or B) equals P(A) plus P(B) minus P(A and B), so 0.60 equals 0.75 minus the joint probability, which gives 0.15. The events are therefore not mutually exclusive.
- A0.15Correct
- B0.75
- C0.135
- D0.25
Explanation
P(A∪B) = P(A) + P(B) − P(A∩B), so 0.60 = 0.75 − P(A∩B), giving 0.15. The option 0.75 ignores the overlap correction, and 0.135 is the product 0.30×0.45, which wrongly assumes independence.
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