1. Simulation

Monty Hall's Three Doors

You are asked to develop a simulation of the Monty Hall Three Door problem. Recall, there are three doors. Behind one is a car and behind two are goats. You choose one of the doors and Monty opens one of the other doors revealing a goat. You are then asked whether you want to change your choice or not. Your goal is to find the car which is behind one of the doors.
You have two decisions to make: which door you believe contains the car and whether you switch or not. You should always choose the same door prior to doing the simulations you will develop. You will then try both decisions regarding switching or not and see which gives you better results-that is, gets you the car more often. The randomness comes about by generating a random number that will correspond to the actual location of the car. Recall, no matter which door has the car, Monty will always be able to reveal a goat behind one of the other doors.
Please do 100 simulations of this problem using excel.
Do you believe the results of the simulation correspond to the best policy? What is the expected number of times you would win the car using the two strategies? Does the simulation back this up?