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Say we have 100 samples, and a first draw results in samples S1,...,S10 being drawn (S1-S10 being distinct samples, as the sampling is without replacement). Now if I put all samples back and draw 10 samples for a second time, how many of the previously drawn samples S1,..,S10 to I expect to draw again?

I understand that I can calculate the probability of drawing say only S1, or S1 and S2 etc., but how do I calculate the expected number of resampling items from S1 to S10?

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    $\begingroup$ Please search our site for hypergeometric (distribution) and capture-recapture. Indeed, a simplified description is illuminating: simply put 90 black balls and 10 red balls in an urn (the latter representing the first sample). What is the distribution of the number of red balls obtained in a simple random sample without replacement from this urn? $\endgroup$
    – whuber ♦
    Commented Aug 10, 2023 at 18:40

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