The beta-binomial model which is generated by a simple mixture model has been widely applied in the social, physical, and health sciences. Lee and Sabavala (1987) proposed a Bayesian approach with a conjugate-type beta family of priors for suitably transformed parameters in the beta-binomial, and demonstrated the simulations for a special case of two trials. The main purpose of this paper is to extend the study of Lee and Sabavala (1987) by a numerical double integration. This method can be used for the case of general trials. When the number of trials is two, the results are similar to those from Lee and Sabavala (1987). However, the predictions for the real problems are much better than the results in Lee and Sabavala (1987).
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