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We throw n identical balls into m urns at random, where each urn is equally likely and each throw is independent of any other throw. What is the probability that the i-th urn is empty?

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Chance of not hitting urn $i$ in any single throw: $\frac{m-1}{m}$,

Chance of not hitting urn $i$ in $n$ consecutive throws: $\left(\frac{m-1}{m}\right)^n$.

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