Tips piratenkapern

2 dice Probabilities of throwing X skulls with two six-sided 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 Probabilities of throwing X skulls with eight six-sided 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% Probabilities of throwing X or more skulls with eight six-sided dice 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%