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At least one six

The probability of at least one six is 1 minus the probability of no sixes. On one dice roll the probability of not a six is 5 out of 6. Two independent rolls give this ratio squared. The fraction 11 out of 36 is the exact value. The course theory rounds the same value to 0.31. Four decimals are written here, so the rounding can be checked against the fraction.

P(at least one)=1−(56)nP(\text{at least one}) = 1 - \left(\frac{5}{6}\right)^nn dice

Symbols

nnnumber of dice

Example

Two dice: 1−(56)2=1136≈0.30561 - \left(\dfrac{5}{6}\right)^2 = \dfrac{11}{36} \approx 0.3056.

The course rounds 11/36 to 0.31. "At least one" is calculated with the complement.
Practise probability for free →

← Independent trials

Part of Mathematics 1P: Probability.