The Monty Hall problem and its generalizations
Alen Kopić · PeFprints (University of Ljubljana) · 2013
The so-called Monty Hall problem in its basic form is a probability puzzle where we initially have three doors, with a car behind one of the doors and goats behind the other two. We first choose one door. The game host, who knows behind which door the car is, then opens remaining door which has a goat behind it and offers us the opportunity to change our initial choice by picking the only remaining closed door. The question is whether it is better to change doors or not. The purpose of this work is to present a solution to the Monty Hall problem in a clear and mathematically correct way and to explore its generalisations in which different numbers of doors, cars and door changes are possible. Also presented are results of computer simulations of Monty Hall problem and its generalisations.