Worked probability tree · printed probabilities
Two draws without replacement
Read the conditional branches and the product for each complete outcome. These values stay fixed to the source example.
Start with 3 green and 2 white counters. Four counters remain after the first draw.
Start · probability 1
Open a branch to follow its outcomes. Outcome percentages are for complete paths. Open an outcome to see its calculation.
G₁ · Green3/5 · 2 outcomes
G₁ · Green
G₂ · GreenPath 30%
G₁ · Green → G₂ · Green- Branch weights
- 3/5 × 2/4
- Complete path probability
- 3/10= 0.3 · 30%
W₂ · WhitePath 30%
G₁ · Green → W₂ · White- Branch weights
- 3/5 × 2/4
- Complete path probability
- 3/10= 0.3 · 30%
W₁ · White2/5 · 2 outcomes
W₁ · White
G₂ · GreenPath 30%
W₁ · White → G₂ · Green- Branch weights
- 2/5 × 3/4
- Complete path probability
- 3/10= 0.3 · 30%
W₂ · WhitePath 10%
W₁ · White → W₂ · White- Branch weights
- 2/5 × 1/4
- Complete path probability
- 1/10= 0.1 · 10%
Compare outcome probabilities
| Outcome | Probability |
|---|---|
| G₁ · Green → G₂ · Green | 3/10= 0.3 · 30% |
| G₁ · Green → W₂ · White | 3/10= 0.3 · 30% |
| W₁ · White → G₂ · Green | 3/10= 0.3 · 30% |
| W₁ · White → W₂ · White | 1/10= 0.1 · 10% |
| All 4 outcomes | 1= 1 · 100% |
Tree assumptions and source notes
Gᵢ and Wᵢ name the colour on draw i, not the identity of an individual counter.
The second draw has four counters left. Update both the colour count and the denominator; the draws are not independent.
GG, GW, WG and WW are complete ordered outcomes. The colour types GG, GW and WW are not equally likely.
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