Plan from the supplied facts
The fictional model supplies two mutually exclusive, exhaustive routes: 75% probability of 2 hours, 25% of 8 hours. These probabilities are teaching inputs, not measured forecasts. Expected effort is the probability-weighted sum; no actual route takes 3.5 hours in this model.
| Route | Probability | Hours | Weighted hours |
|---|---|---|---|
| Short | 0.75 | 2 | 1.5 |
| Long | 0.25 | 8 | 2 |
| Total | 1 | Either 2 or 8 | 3.5 |
Work through the choice
0.75×2+0.25×8=3.5 is an average over the supplied model. A promise to finish within 3.5 hours would fail whenever the long route occurs.
If the long-route probability becomes 0.5, keeping the two route hours fixed, what is expected effort?
Show the worked answer
0.5×2+0.5×8=5 hours. The possible realised outcomes remain 2 and 8 hours.
Material to use in your plan
Use one row per exclusive route with probability, conditional hours and product. Require probabilities to sum to one; show possible outcomes beside the expected value.