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

A risk analyst defines two events for a loan portfolio over the next year: A = 'the borrower defaults' and B = 'the borrower's rating is upgraded.' Assume a borrower cannot both default and be upgraded in the same year, with P(A) = 0.04 and P(B) = 0.10. What is the probability that the borrower either defaults or is upgraded?

The probability is 0.14. Because default and upgrade cannot occur together, the intersection has zero probability, so the union is just the sum of the individual probabilities: 0.04 plus 0.10 equals 0.14.

  1. A0.140Correct
  2. B0.144
  3. C0.136
  4. D0.060

Explanation

A and B are mutually exclusive, so P(A or B) = P(A) + P(B) = 0.04 + 0.10 = 0.14. Option 0.136 subtracts the product 0.004 as if the events were independent and not exclusive, which is wrong because P(A and B) = 0. Option 0.060 subtracts the probabilities instead of adding.

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