The Monty Hall Problem

Definition

Monty Hall problem is a mathematical brain teaser dealing with probabilistic decision making. It originated from a TV show hosted by Monty Hall in 1963. It is a very good example of how probabilistic scenarios may seem simple but yet at times can be difficult to wrap our minds around them.¹

Who

This problem is recommended for anyone interested in statistics, especially Bayes Theorem. Enjoy!

What

The problem is simple, you go to Monty’s game show “Let’s make a deal”. There are 3 doors in front of you. Behind 1 of those doors, there is a car and behind the remaining two doors are goats! If you select the door behind which the car is there, you drive it home. The host asks you to select a door, you pick one. Then comes the fun part. After you picked a door, the host will open one of the two remaining doors to always reveal a goat. Now he would ask you, are you going to switch your selection or are you staying with your original choice? This is where the dilemma kicks in.¹

Why

The solution to Monty Hall problem seems weird because our mental assumptions for solving the problem do not match the actual process. Our mental assumptions were based on independent, random events. However, Monty knows the prize location and uses this knowledge to affect the outcomes in a non-random fashion. Once you understand how Monty uses his knowledge to pick a door, the results make sense.²

See Theoretical Knowledge Vs Practical Application.

How

Many of the References and Additional Reading websites, and Videos will assist you with understanding the Monty Hall Problem.

As some professors say: “It is intuitively obvious to even the most casual observer.”

References

¹ “Monty Hall Problem — An Empirical Proof”. 2021. Medium. https://towardsdatascience.com/monty-hall-problem-an-empirical-proof-60e7e0761503.

² Frost, Jim. 2017. “The Monty Hall Problem: A Statistical Illusion”. Statistics By Jim. https://statisticsbyjim.com/fun/monty-hall-problem/.

Additional Reading

Huber, Mark. “The Monty Hall Problem”. 2013. www1.cmc.edu. https://www1.cmc.edu/pages/faculty/MHuber/Research/talks/huber_talk_2013d.pdf.

“Marilyn Vos Savant | The Game Show Problem (Printer-Friendly)”. 2022. web.archive.org. https://web.archive.org/web/20100928000559/http://marilynvossavant.com/articles/gameshow_print.html?t=64.

“The Monty Hall Problem”. 2021. Medium. https://www.cantorsparadise.com/the-monty-hall-problem-6e3e56e454a2.

“The Monty Hall Problem”. 2019. Medium. https://medium.com/swlh/the-monty-hall-problem-3383e3048aa8.

“Monty Hall Problem | Brilliant Math & Science Wiki”. 2022. brilliant.org. https://brilliant.org/wiki/monty-hall-problem/.

“Monty Hall Problem | Understand Monty Hall Problem In Detail”. 2019. EDUCBA. https://www.educba.com/monty-hall-problem/.

“The Monty Hall Problem – Math Images”. 2022. mathimages.swarthmore.edu. https://mathimages.swarthmore.edu/index.php/The_Monty_Hall_Problem.

“Monty Hall Problem – Wikipedia”. 2022. en.wikipedia.org. https://en.wikipedia.org/wiki/Monty_Hall_problem.

“🐐 Monty Hall Problem Simulator”. 2022. montyhall.io. https://montyhall.io/.

Vazsonyi, Andrew. “Which Door Has the Cadillac?” 2022. web.archive.org. https://web.archive.org/web/20140413131827/http://www.decisionsciences.org/DecisionLine/Vol30/30_1/vazs30_1.pdf.

Videos