Plan from the supplied facts
The fictional plan proceeds only if independent checks A and B both pass. A costs 2 hours and passes with probability 0.5; B costs 1 and passes with probability 0.9. Stop immediately on failure. Probabilities and perfect check results are original model assumptions.
| Order | First check cost | Chance second needed | Expected total h |
|---|---|---|---|
| A then B | 2 | 0.5 | 2 + 0.5×1 = 2.5 |
| B then A | 1 | 0.9 | 1 + 0.9×2 = 2.8 |
| Both always | 3 total | 1 | 3 |
Work through the choice
Only the first pass probability controls whether the second check is performed. Choosing by first-check price alone ignores the chance of stopping.
Which order has lower expected effort, and by how much?
Show the worked answer
A then B: 2.5 versus 2.8, saving 0.3 expected hours. An individual completed inquiry may still use all three hours.
Material to use in your plan
For each proposed order, record first cost + first pass probability × second cost. Include conditional probabilities or further branches if the checks are not independent.