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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A risk manager models the number of loan defaults in a portfolio of 10 independent loans, each with a default probability of 0.10. What is the probability that exactly 2 loans default?

The probability is 0.1937. With 10 independent loans and default probability 0.10, the binomial formula gives 45 × 0.1^2 × 0.9^8, which equals about 0.1937. The combination factor of 45 counts the ways to choose which two loans default.

  1. A0.1937Correct
  2. B0.2639
  3. C0.0574
  4. D0.3487

Explanation

Binomial: C(10,2)=45. P = 45 × 0.1^2 × 0.9^8 = 45 × 0.01 × 0.43047 = 0.1937. The 0.3487 option is P(0 defaults) = 0.9^10. The 0.0574 option omits the combinatorial factor, giving about 0.0043 times a wrong power and is not correct.

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