Monty Hall Problem Analysis

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Mathematical Exploration

Probability and the Exploration of the Monty Hall Problem

Candidate Name: Tomass Pildegovičs
Candidate Number: 001001-0022
School Name: Riga State Gymnasium No. 1
Exam Session: May 2015

Table of Contents

Introduction 2
Solving the standard Monty Hall Problem 3
Solving modified versions of the Monty Hall Problem 4 Solving Fundamentally altering the conditions of the problem
Possible applications 9
Conclusion 9

Introduction

Monty Hall’s television game show Let’s Make a Deal gained widespread popularity in the 1960s and 1970s amongst the American audience. The set of this show would become the basis of one of the
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This claim was met with much controversy, as thousands of academics sent letters in which they voiced their staunch disagreement and accused vos Savant of propagating mathematical fallacy. Her answer -- that the contestant should switch doors -- has been debated in the halls of the Central Intelligence Agency and the barracks of fighter pilots in the Persian Gulf. It has been analyzed by mathematicians at the Massachusetts Institute of Technology and computer programmers at Los Alamos National Laboratory in New Mexico. It has been tested in classes from second grade to graduate level at more than 1,000 schools across the country. The correct solution to The Monty Hall Problem is to such a great extent counterintuitive, that it can be difficult to believe; yet it remains unwaveringly true. The aim of this investigation is to examine the solutions to this legendary problem in order to establish a general pattern, while exploring numerous variations of the original problem.

Solving the standard Monty Hall Problem

In order to attempt to solve the Monty Hall Problem, it is necessary to establish four key assumptions: The participant is attempting to win the car, not the goats. The host must always offer the chance to switch between the originally chosen door and the remaining closed door. The host must always open a door that was not first chosen by the
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Solving modified versions of the Monty Hall Problem

What if the set of the show had 4 doors?

There are now four doors to choose from, with one of the doors concealing a car and the other three doors concealing goats. The same four previously established key conditions still hold true.

Door 1 Door 2 Door 3 Door 4

Once again the participant has two options available: to stay with the first choice or to switch once the host has revealed one of the doors concealing a goat.

Option 1: Participant decides to stick with the initial choice. As there are 4 doors and only one of them conceals a car, the probability that it is the initially chosen door is p(x)=1/4 or 25%. Just as in the case with 3 doors the probability of the car being behind the initially chosen door does not change over the course of the
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