FRM Part I · FRM Exam Part I · Fundamentals of Probability
Two counterparties default independently over one year with probabilities 4% and 10%. Given that at least one of them defaults, what is the probability, to three decimals, that both default?
The conditional probability is about 0.029, and 0.028 is the closest option. Joint default is 0.04 x 0.10 = 0.004, at least one default is 0.136, and 0.004/0.136 is roughly 0.0294. Using 0.004 alone ignores conditioning on at least one default.
- A0.004
- B0.040
- C0.100
- D0.028Correct
Explanation
P(both) = 0.04 x 0.10 = 0.004. P(at least one) = 0.04 + 0.10 - 0.004 = 0.136. Conditional probability = 0.004/0.136 = 0.0294, which rounds to 0.029, so closest is 0.028? Recomputing exactly: 0.004/0.136 = 0.02941.
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