FRM Part I · FRM Exam Part I · Fundamentals of Probability
A bank classifies a loan's outcome over one year into three mutually exclusive and exhaustive events: Default (D), Downgrade without default (G), and Neither (N). The probability of default is 2% and the probability of downgrade without default is 7%. What is the probability that the loan is not downgraded and does not default?
The probability is 91%. Since default, downgrade without default, and neither form a mutually exclusive and exhaustive set, their probabilities sum to 100%. Subtracting 2% and 7% from 100% leaves 91% for the loan neither defaulting nor being downgraded.
- A91%Correct
- B93%
- C98%
- D9%
Explanation
Because the three events are mutually exclusive and exhaustive, probabilities sum to 1. P(N) = 1 - 0.02 - 0.07 = 0.91. Answer 93% results from subtracting only the 7% downgrade probability. Answer 9% is P(D)+P(G), which is the complement of N.
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