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For the rules of piraten kapern, see GameHelpPiratenKapern
Probabilities
Binomial formula
n! × pᵏ(1 − p)ⁿ⁻ᵏ k!(n-k)!
n: number of trails (dice thrown) k: number of successes (dice with a face value)p: probability of success (of a die face value)
Example
Probability of throwing 3 with 5 dice:
5! × (⅙)³ × (1 − ⅙)⁵⁻³ 3!(5-3)!
= 5×4×3×2×1 × (⅙)³ × (⅚)² 3×2×1 × 2×1
= 10 × (⅙)³ × (⅚)²≈ 0.0321 or 3.21%
2 dice
| In words | In maths | Percentage |
|---|---|---|
| Probability of no skulls | P(X = 0) = (⅚)² | ≈ 69.4% |
| Probability of one skull | P(X = 1) = 2 × (⅙) × (⅚) | ≈ 27.8% |
| Probability of two skulls | P(X = 2) = (⅙)² | ≈ 2.78% |
8 dice
| In words | In maths | Percentage |
|---|---|---|
| Probability of no skulls | P(X = 0) = (⅚)⁸ | ≈ 23.3% |
| Probability of one skull | P(X = 1) = 8 × (⅙) × (⅚)⁷ | ≈ 37.2% |
| Probability of two skulls | P(X = 2) = 28 × (⅙)² × (⅚)⁶ | ≈ 26.0% |
| Probability of three skulls | P(X = 3) = 56 × (⅙)³ × (⅚)⁵ | ≈ 10.4% |
| Probability of four skulls | P(X = 4) = 70 × (⅙)⁴ × (⅚)⁴ | ≈ 2.60% |
| In words | In maths | Percentage |
|---|---|---|
| Probability of one or more skulls | P(X ≥ 1)
= 1 − P(X = 0) = 1 − (⅚)⁸ |
≈ 76.7% |
| Probability of two or more skulls | P(X ≥ 2)
= 1 − [ P(X = 0) + P(X = 1) ] = 1 − [ (⅚)⁸ + 8 × (⅙) × (⅚)⁷ ] |
≈ 39.5% |
| Probability of three or more skulls | P(X ≥ 3)
= 1 − [ P(X = 0) + P(X = 1) + P(X = 2) ] = 1 − [ (⅚)⁸ + 8 × (⅙) × (⅚)⁷ + 28 × (⅙)² × (⅚)⁶ ] |
≈ 13.5% |
| Probability of four or more skulls | P(X ≥ 4)
= 1 − [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ] = 1 − [ (⅚)⁸ + 8 × (⅙) × (⅚)⁷ + 28 × (⅙)² × (⅚)⁶ + 56 × (⅙)³ × (⅚)⁵ ] |
≈ 3.07% |
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