Suppose we have a bag of n different balls, and each time m (m<n) balls are taken out for checking from the bag and put back. How many times on average of this experiment are needed that all the balls will be checked for at least one time?
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1$\begingroup$ mathoverflow.net/questions/13171/… $\endgroup$– Douglas ZareCommented May 31, 2011 at 17:30
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The magic words are "coupon collector problem".
answered May 31, 2011 at 16:10
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$\begingroup$ ... although the standard coupon collector problem has one coupon collected at a time. Having $m > 1$ makes it more complicated. A Markov chain approach with states corresponding to the number of balls that have been checked should be straightforward, although I don't know if a closed-form formula is available. $\endgroup$ Commented May 31, 2011 at 17:14