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The beta distribution is conjugate prior for the binomial distribution.

Is the beta-binomial distribution a conjugate prior for some sampling distribution?

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You're looking for the hypergeometric distribution. Incidentally, this link is one of the first two hits on Google for "beta binomial" "conjugate prior".

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Have a look at the wikipedia page, there's a very nice conjugate prior table there.

If you are working with python, you can import the conjugate_prior package and start hacking

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