Worked probability tree · printed probabilities
Fuel type, then tank filling
Read the conditional branches and the product for each complete outcome. These values stay fixed to the source example.
Each full/not-full probability is conditional on the fuel type.
Start · probability 1
Open a branch to follow its outcomes. Outcome percentages are for complete paths. Open an outcome to see its calculation.
L · Leaded0.3 · 2 outcomes
L · Leaded
F · FullPath 7.5%
L · Leaded → F · Full- Branch weights
- 0.3 × 0.25
- Complete path probability
- 3/40= 0.075 · 7.5%
F′ · Not fullPath 22.5%
L · Leaded → F′ · Not full- Branch weights
- 0.3 × 0.75
- Complete path probability
- 9/40= 0.225 · 22.5%
U · Unleaded0.6 · 2 outcomes
U · Unleaded
F · FullPath 12%
U · Unleaded → F · Full- Branch weights
- 0.6 × 0.2
- Complete path probability
- 3/25= 0.12 · 12%
F′ · Not fullPath 48%
U · Unleaded → F′ · Not full- Branch weights
- 0.6 × 0.8
- Complete path probability
- 12/25= 0.48 · 48%
D · Diesel0.1 · 2 outcomes
D · Diesel
F · FullPath 3%
D · Diesel → F · Full- Branch weights
- 0.1 × 0.3
- Complete path probability
- 3/100= 0.03 · 3%
F′ · Not fullPath 7%
D · Diesel → F′ · Not full- Branch weights
- 0.1 × 0.7
- Complete path probability
- 7/100= 0.07 · 7%
Compare outcome probabilities
| Outcome | Probability |
|---|---|
| L · Leaded → F · Full | 3/40= 0.075 · 7.5% |
| L · Leaded → F′ · Not full | 9/40= 0.225 · 22.5% |
| U · Unleaded → F · Full | 3/25= 0.12 · 12% |
| U · Unleaded → F′ · Not full | 12/25= 0.48 · 48% |
| D · Diesel → F · Full | 3/100= 0.03 · 3% |
| D · Diesel → F′ · Not full | 7/100= 0.07 · 7% |
| All 6 outcomes | 1= 1 · 100% |
Tree assumptions and source notes
L, U and D partition customers by fuel type; F means a full tank.
Multiply along a fuel/fullness path and add disjoint fuel paths. P(F | U) is not P(U | F).
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