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Boxcars


Boxcars

A roll of two 6s (the highest roll possible) on a pair of 6-sided dice. The probability of rolling boxcars in a single roll of two dice is 1/36, or 2.777...%.

In order to have a 50% chance of obtaining at least one boxcars in n rolls of two dice, it must be true that

 1-((35)/(36))^n=1/2,
(1)

so solving for n gives

 n=(ln2)/(ln36-ln35)=24.605....
(2)

In fact, rolling two dice 25 times gives a probability of

 1-((35)/(36))^(25) approx 0.505532
(3)

that at least once boxcars will occur.


See also

Craps, Dice, Eighter from Decatur, de Méré's Problem, Quincunx, Snake Eyes

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References

Mosteller, F. Fifty Challenging Problems in Probability with Solutions. New York: Dover, p. 3, 1987.

Referenced on Wolfram|Alpha

Boxcars

Cite this as:

Weisstein, Eric W. "Boxcars." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Boxcars.html

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