Decision Making under Risk and Looking for the Optimal Strategies Based on the Available Information

In this paper, we will study the case of decision theory under risk and searching the optimal strategies which guarantee the maximum profits and minimum lost for the decision maker, In particular, we will study the random events which are under specific probability distribution. Based on the available information we will find the posterior distribution for the events using the Bayes’ rule. So we will try to find a mathematical method to minimize the risk rate.