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For the rules of piraten kapern, see GameHelpPiratenKapern
Probabilities
Binomial formula
n! Γ pα΅(1 β p)βΏβ»α΅ 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! Γ (β )Β³ Γ (1 β β )β΅β»Β³ 3!(5-3)!
= 5Γ4Γ3Γ2Γ1 Γ (β )Β³ Γ (β )Β² 3Γ2Γ1 Γ 2Γ1
= 10 Γ (β )Β³ Γ (β )Β²β 0.0321 or 3.21%
2 dice
| In words | In maths | Percentage |
|---|---|---|
| Probability of no skulls | P(X = 0) = (β )Β² | β 69.4% |
| Probability of one skull | P(X = 1) = 2 Γ (β ) Γ (β ) | β 27.8% |
| Probability of two skulls | P(X = 2) = (β )Β² | β 2.78% |
8 dice
| In words | In maths | Percentage |
|---|---|---|
| Probability of no skulls | P(X = 0) = (β )βΈ | β 23.3% |
| Probability of one skull | P(X = 1) = 8 Γ (β ) Γ (β )β· | β 37.2% |
| Probability of two skulls | P(X = 2) = 28 Γ (β )Β² Γ (β )βΆ | β 26.0% |
| Probability of three skulls | P(X = 3) = 56 Γ (β )Β³ Γ (β )β΅ | β 10.4% |
| Probability of four skulls | P(X = 4) = 70 Γ (β )β΄ Γ (β )β΄ | β 2.60% |
| In words | In maths | Percentage |
|---|---|---|
| Probability of one or more skulls | P(X β₯ 1)
= 1 β P(X = 0) = 1 β (β )βΈ |
β 76.7% |
| Probability of two or more skulls | P(X β₯ 2)
= 1 β [ P(X = 0) + P(X = 1) ] = 1 β [ (β )βΈ + 8 Γ (β ) Γ (β )β· ] |
β 39.5% |
| Probability of three or more skulls | P(X β₯ 3)
= 1 β [ P(X = 0) + P(X = 1) + P(X = 2) ] = 1 β [ (β )βΈ + 8 Γ (β ) Γ (β )β· + 28 Γ (β )Β² Γ (β )βΆ ] |
β 13.5% |
| Probability of four or more skulls | P(X β₯ 4)
= 1 β [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ] = 1 β [ (β )βΈ + 8 Γ (β ) Γ (β )β· + 28 Γ (β )Β² Γ (β )βΆ + 56 Γ (β )Β³ Γ (β )β΅ ] |
β 3.07% |
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