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Keep default as the event of interest
This fictional credit scenario supplies odds against default, not an empirical default estimate. “Against” assigns the larger weight to no default. For default itself, the favourable weight is therefore 1 and the unfavourable weight is 9.
Normalize the two weights
The total weight is 10. Default occupies one of those ten units and no default occupies nine. The two probabilities sum to one.
| Outcome | Weight | Normalized probability |
|---|---|---|
| Default | 1 | 1/10 = 10% |
| No default | 9 | 9/10 = 90% |
| Total | 10 | 100% |
Explain why 90% answers the opposite question
Computing 9/(9 + 1) gives the probability of no default under the stated quote. That calculation is arithmetically correct but labels the event incorrectly if presented as default probability. Read the direction before choosing the numerator.
Use a probability only with a matching model
If a later expected-loss exercise uses this converted probability, the default horizon and the other loss inputs must be stated consistently. The odds conversion alone supplies neither loss given default nor exposure at default.