  Total probability and Bayes formula are two basic tools for using prior
information in the Bayesian statistics. In this paper we introduce an
alternative tool for using prior information. This new toold enables us to
improve some traditional results in statistical inference. However, as far as
the authors know, there is no work on this subject, except [1]. The results of
this paper can be extended to other branches of probability and statistics. In
Section 2 total probability formula based on median is defined and its basic
properties are proved. A few applications of this new tool are given in Section
3.
