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    IBHardProbability10–12

    How Many Rolls for a Six with 99% Confidence

    Quantos Lançamentos para um Seis com 99% de Confiança

    A fair six-sided die is rolled nn times. Find the smallest nn for which the probability of getting at least one six is at least 0.990.99.

    "At least one" over many trials is a long sum, but its opposite is a single product. Once the inequality is in that form, the unknown is an exponent and needs logarithms — and the direction of the inequality deserves attention when you divide by a negative logarithm.

    Solution

    Step 1 of 7

    1. 1.Work with the complement — no six at all: