how many numbers drawn more than once There are 100 numbered balls in an urn. We make 100 random draws with replacement. Of course, we can not expect to draw every number exactly once, there will be multiples. What is the expected value of multiply drawn numbers?
I asked this question before (expect number of multipe draws), but the obtained answer does not seem to be correct. 
For a deeper understanding think of just 2 balls and 2 draws: Then the probability of multiples is 50%. The answers given so far focussed on the probability that a fixed number is drawn at least twice, which is 25%.

The chance that a particular number is not drawn at all is $(\frac{99}{100})^{100}$.
The chance that a particular number is drawn exactly once is $\binom{100}{1}\frac{1}{100}(\frac{99}{100})^{99}$.
Now you can find the chance that a particular number is multiply drawn. (Interestingly, this never differs by much from $\frac14$, which is the value in the case of just $2$ balls).
Multiply by $100$ to get the expected count of such numbers (thanks to additivity of expectation).
