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de Mere's Problem

The probability of getting at least one ``6'' in four rolls of a single 6-sided Die is

1-\left({{\textstyle{5\over 6}}}\right)^4 =0.518\ldots,
\end{displaymath} (1)

which is slightly higher than the probability of at least one double 6 in 24 throws,
1-\left({{\textstyle{35\over 36}}}\right)^{24}=0.491.\ldots
\end{displaymath} (2)

de Mere suspected that (1) was higher than (2). He posed the question to Pascal, who solved the problem and proved de Mere correct.

See also Dice


Kraitchik, M. ``A Dice Problem.'' §6.2 in Mathematical Recreations. New York: W. W. Norton, pp. 118-119, 1942.

© 1996-9 Eric W. Weisstein