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Check each estimate on its own
Values of 0.15 and 0.40 each satisfy the probability bounds; 1.05 does not. Passing the individual bound check is necessary but does not prove that a complete collection of stated probabilities is consistent.
Define a complete non-overlapping set
For a fictional next-period rate model, the events rise, remain unchanged and fall cover every stated direction and do not overlap. Assigning probabilities 0.40, 0.35 and 0.25 gives a total of one. This is a discrete exercise, not a central-bank forecast.
| Scenario | Probability |
|---|---|
| Rise | 40% |
| Unchanged | 35% |
| Fall | 25% |
| Total | 100% |
Do not impose that sum on overlapping events
The event “rates rise” and the event “a bond fund has a positive return” can overlap. Their probabilities are not required to sum to one simply because two estimates are listed together. To calculate their union, account for the overlap.
Separate missing coverage from invalid individual values
If only rise and unchanged are listed with the probabilities above, their sum is 75%. Those two probabilities can each be valid while the list remains incomplete. The model needs the fall scenario or an explicit explanation of the omitted outcomes.