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How is the following formula derived which yields the probability that the sum of the squares of n random draws from the closed interval [-1,1] is less than one?

formula: (1/2^n)*pi^(n/2)/(n/2)!

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I suspect Stirling's formula is involved, since $\pi$ and factorials appear. But I also suspect this is closer to being an exercise than a research question, especially since you seem sure of the formula. So this question might be more appropriate for stackexchange or maybe Wikipedia's mathematics reference desk than for mathoverflow. –  Michael Hardy Jun 12 '11 at 18:56
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1 Answer

up vote 5 down vote accepted

Volume of the ball divided by volume of the cube.

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