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FRM Part I · FRM Exam Part I · Fundamentals of Probability

A risk analyst models two events for a bank: Event A is that a corporate borrower defaults within one year, with P(A) = 0.04, and Event B is that a commodity price index falls by more than 20%, with P(B) = 0.10. If A and B are independent, what is the probability that at least one of the two events occurs?

The probability that at least one event occurs is 0.136. Independence gives a joint probability of 0.004, and the union is 0.04 plus 0.10 minus 0.004. Simply adding the two probabilities to get 0.140 double counts the overlap.

  1. A0.136Correct
  2. B0.140
  3. C0.004
  4. D0.144

Explanation

For independent events, P(A and B) = 0.04 × 0.10 = 0.004. P(A or B) = 0.04 + 0.10 − 0.004 = 0.136. The option 0.140 omits subtracting the joint probability, double counting the overlap.

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