This article proposes some related issues to classification problem by Bayesian method for two populations. They are relationships between Bayes error (BE) and other measures and the results for determining the BE. In addition, we propose three methods to find the prior probabilities that can make to reduce BE. The calculation of these methods can be performed conveniently and efficiently by the MATLAB procedures. The new approaches are tested by the numerical exam- ples including synthetic and benchmark data and applied in medicine and economics. These examples also show the advantages of the proposed methods in comparison with existing methods.