Ronghua Zhang wrote:
>Suppose there exist N distinct objects, each time get n objects out
>of them(these n objects must be different) and then put them back,
>keep sampling for k rounds, and at last, what is the
>probability of at least x distinct objects have been
>selected at least once?
Look at the complementary event: what is the probability P
that exactly N - x distinct objects have not been selected?
Then the probability you seek is 1 - P .
>Yes, I'v already thought of that. But the complement probability is also
>hard for me. Can you help me?
Let x be fixed; when you make one pick of n objects out of N distinct
objects, what is the probability that none of N - x distinct objects has
been selected?
Replace the n objects, mix well, and pick again. What is the probability
that none of those same N - x distinct objects has been selected?
Repeat this procedure k times.
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