In this paper, we considerkhypergeometric populationsπi= π(Mi,mi,si),i=1,…,k,whereMiis the number of units in populationπi,miis the number of units selected fromπi,andsiis the number of defective units inπi. Let. A populationπiwithis considered as a best population. We are interested in selecting the best population and the best population compared with a control. It is assumed that the unknown parameteressii = 1,…,k, follow some binomial prior distribution with unknown hyperparameters. Under the hypergeometric-binomial model, two empirical Bayes selection rules are studied according to the different selection problems. It is shown that for each empirical Bayes selection rule, the corresponding Bayes risk tends to the minimum Bayes risk with a rate of convergence of orderO(exp(-cn))for some positive constantc, where the value ofcvaries depending on the rule andnis the number of accumulated past observations.