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# I have an unlimited supply of standard 6-sided dice

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I have an unlimited supply of standard 6-sided dice. What's the fewest number of dice that I have to simultaneously roll to be at least 95% likely to roll at least one 6?

Oct 27, 2020

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You need to roll 17 dice to get the probability of 95.5% of getting at least one 6.

Oct 27, 2020
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I have an unlimited supply of standard 6-sided dice. What's the fewest number of dice that I have to simultaneously roll to be at least 95% likely to roll at least one 6?

$$1-\left(\frac{5}{6}\right)^n>0.95\\ 0.05>\left(\frac{5}{6}\right)^n\\ log(0.05)>log\left(\frac{5}{6}\right)^n\\ log(0.05)>nlog\left(\frac{5}{6}\right)\\ nlog\left(\frac{5}{6}\right) \frac{log(0.05)}{log\left(\frac{5}{6}\right)}\\ n>16.43\\~\\ smallest\;\;n=17$$

Oct 27, 2020