FRM Part I · FRM Exam Part I · Common Univariate Random Variables
A bank's loan portfolio contains 10 independent loans, each with a 5% probability of default over one year. What is the probability that exactly one loan defaults? (Use 0.95^9 = 0.6302.)
The probability is 0.3151. With 10 independent loans and a 5% default chance, the binomial formula gives 10 x 0.05 x 0.95^9, which equals 0.3151. The factor of 10 counts the ways to choose which loan defaults.
- A0.3151Correct
- B0.5000
- C0.0500
- D0.6302
Explanation
Binomial: P(X=1) = C(10,1) x 0.05 x 0.95^9 = 10 x 0.05 x 0.6302 = 0.3151. Option 0.6302 omits the combinatorial factor and probability term, giving only 0.95^9, which is the probability of one particular loan defaulting only partly.
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