A total of n balls, numbered 1 through n, are put into n urns, also numbered 1 through n in such a way that ball i is equally likely to go into any of the urns 1, 2, . . . , i. Find the expected number of urns that are empty if n=100
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Since there are n urns and each ball has a $\frac{1}{n}$ chance of going into any specific urn, the probability that a ball does not go into a specific urn is $1 - \frac{1}{n}$. Since there are n balls, the probability that none of the balls go into a specific urn Show more…
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A total of $n$ balls, numbered 1 through $n$, are put into $n$ urns, also numbered 1 through $n$ in such a way that ball $i$ is equally likely to go into any of the urns $1,2, \ldots$, . Find (a) the expected number of urns that are empty; (b) the probability that none of the urns is empty.
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