Mounty Hall Problem as an Example of Bayes Formula

Abstract

Bayes formula is a tool used to calculate the condition probability of the event under different situations. This article is used to investigate the principle and the application of the Bayes formula, which belongs to the statistics and mathematics. The Mounty Hall problem is a classic example of application of the Bayes formula. The problem is whether the probability to choose the supercar would increase if the guest shifts his choice. To conquer this problem, this article aims to calculate the conditional probability by Bayes formula. In doing so, one can evaluate the probability of after shifting the door easily. In addition, the article also aims to prove the result via the Bayes formula. The author uses two methods to prove the result. One is the simulation. The author uses the statistical software——excel to do simulation, collect the data, and calculate the final result. Next, the author compares the result with the calculation result. Then, the author use t-test to prove the two results are the same. The second method is programing. The result and conclusion of the article is that the Baye’s formula do have the function to calculate the complex probability. The Bayes formula is practical. The significance of the article is to provide different ways to prove the result of the simulation.