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Dice Rolls as an Example of the Coupon Collector's Problem

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This Demonstration shows an example of the "coupon collector's problem": you roll fair -sided dice until all possible sums appear.

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Using Monte Carlo simulation, the Demonstration estimates

• the expected number of rolls needed to get all possible sums and the number of rolls needed for selected confidence levels (top table).

• the histogram of the number of rolls needed (upper graph).

• the distribution of totals when rolling the specified dice (lower graph).

If you increase the number of iterations, you get more accurate estimates, but this requires more computational effort and time.

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Contributed by: Michail Bozoudis (August 2014)
Suggested by: Michail Boutsikas
Open content licensed under CC BY-NC-SA

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