We want to accept or reject a finite population with reliability demonstration test. In this paper, we will describe Bayesian approaches for the reliability demonstration test based on the samples from a finite population. The Bayesian method is an approach that prior distribution and likelihood function combine to from posterior distribution. When we select somethings in a samples, we consider hypergeometric distribution. In this paper, we will explain the conjugacy of the beta-binomial distribution and hypergeometric distribution. The purpose of this paper is to make a decision between accept and reject in a finite population based on the conjugacy of the beta-binomial distribution.