Re: Placing Balls in Urns and Expected values

In article <1166092677.142803.243940@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Taria" <mchew02@xxxxxxxxxxx> wrote:
Suppose that n balls are randomly placed in n urns in such a way that
each ball is equally to go into each urn. What are the expected number
of empty urns.

The probability that a particular ball will not be in urn 1 is 1-1/n.
So the probability that no balls are in urn 1 is (1-1/n)^n. That is
the expectancy of urn 1 being empty is (1-1/n)^n. This means that the
expected number of empty urns is n (1-1/n)^n.

Rob Johnson <rob@xxxxxxxxxxxxxx>
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