The Monty Hall Problem

Introduction

The Monty Hall problem is a famous little puzzle from a game show. It goes like this: you are presented with 3 doors. Behind two are goats and behind the third is a car. You are asked to select a door; if you select the door with the car, you win! After selecting, the host then opens one of the remaining two doors, revealing a goat. The host then asks if you would like to switch doors or stick with your original choice. What would you do? Does it matter?

Objectives

In this lab you will:

• Use Bayes' theorem along with a simulation to solve the Monty Hall problem

Run a simulation

This is not a traditional application of Bayes' theorem, so trying to formulate the problem as such is tricky at best. That said, the scenario does capture the motivating conception behind Bayesian statistics: updating our beliefs in the face of additional evidence. With this, you'll employ another frequently used tool Bayesians frequently employ, running simulations. To do this, generate a random integer between one and three to represent the door hiding the car. Then, generate a second integer between one and three representing the player's selection. Then, of those the contestant did not choose, select a door concealing a goat to reveal. Record the results of the simulated game if they changed versus if they did not. Repeat this process a thousand (or more) times. Finally, plot the results of your simulation as a line graph. The x-axis should be the number of simulations, and the y-axis should be the probability of winning. (There should be two lines on the graph, one for switching doors, and the other for keeping the original selection.)

# Your code here

Summary

In this lab, you further investigated the idea of Bayes' theorem and Bayesian statistics in general through the Monty Hall problem. Hopefully, this was an entertaining little experience!