Mathematical problems | Probability problems | Decision-making paradoxes | Probability theory paradoxes
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from reader Craig F. Whitaker's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? Vos Savant's response was that the contestant should switch to the other door. Under the standard assumptions, the switching strategy has a 2/3 probability of winning the car, while the strategy that remains with the initial choice has only a 1/3 probability. When the player first makes their choice, there is a 2/3 chance that the car is behind one of the doors not chosen. This probability does not change after the host reveals a goat behind one of the unchosen doors. When the host provides information about the 2 unchosen doors (revealing that one of them does not have the car behind it), the 2/3 chance of the car being behind one of the unchosen doors rests on the unchosen and unrevealed door, as opposed to the 1/3 chance of the car being behind the door the contestant chose initially. The given probabilities depend on specific assumptions about how the host and contestant choose their doors. A key insight is that, under these standard conditions, there is more information about doors 2 and 3 than was available at the beginning of the game when door 1 was chosen by the player: the host's deliberate action adds value to the door he did not choose to eliminate, but not to the one chosen by the contestant originally. Another insight is that switching doors is a different action from choosing between the two remaining doors at random, as the first action uses the previous information and the latter does not. Other possible behaviors of the host than the one described can reveal different additional information, or none at all, and yield different probabilities. Many readers of vos Savant's column refused to believe switching is beneficial and rejected her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them calling vos Savant wrong. Even when given explanations, simulations, and formal mathematical proofs, many people still did not accept that switching is the best strategy. Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating vos Savant's predicted result. The problem is a paradox of the veridical type, because the solution is so counterintuitive it can seem absurd but is nevertheless demonstrably true. The Monty Hall problem is mathematically closely related to the earlier Three Prisoners problem and to the much older Bertrand's box paradox. (Wikipedia).
Monty Hall, yeah yeah, but with me. It's a mathematical curiosity and, in general, maths is intuitive - an important statement which we cut out of the video.
From playlist My Maths Videos
Monty Hall II: Revenge of Monty Hall
This is a follow-up to my original video on the Monty Hall Problem. Monty has realised we've worked it out and is tired of people always swapping doors and winning so often. So he has an idea... The original gameshow was called "Let's Make A Deal", hosted by Monty Hall. Monty didn't alw
From playlist My Maths Videos
Monty Hall Problem (best explanation) - Numberphile
Another pass at the Monty Hall Problem - see the last video and a new "express explanation" at: http://bit.ly/MontyHallProb More links & stuff in full description below ↓↓↓ Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberph
From playlist Monty Hall Problem on Numberphile
The Monty Hall Problem: Switch Doors or Not?
#shorts This video presents a problem related to the famous Monty Hall Problem.
From playlist Math Shorts
Can Probability Violate Causality?
The Monty Hall problem is famous in probability and has been discussed at length over the years. While the actual solution is simple, the interesting part is exploring deeper connections to philosophy and metaphysics. In part 1, I explore the problem and why people get it wrong, and in par
From playlist Summer of Math Exposition Youtube Videos
History of science 6: The Monty Hall problem
This video describes the history and solution of the Monty Hall problem, a notorious problem in probability theory that even mathematicians often get wrong.
From playlist History of science
The Monty Hall Problem: Switch Doors or Not?
This video explains the Monty Hall problem.
From playlist Mathematics General Interest
The Monty Hall Problem (2 of 2: Explanation)
via YouTube Capture
From playlist Mathematical Exploration
The Easiest Problem Everyone Gets Wrong
We know how difficult the Monty Hall Problem is for so many people even after they’re shown all the math behind the best possible strategy. It’s basic probability, but it’s deceptive -- and it all started with the Bertrand’s Box Paradox. In this video, I go back to the origins of a probab
From playlist Prob and Stats
Coding Challenge 170: The Monty Hall Problem
It's the Monty Hall Problem! In JavaScript! With p5.js! Yes, you really double your chances of winning by switching doors. I hope to convince you of this in this video! https://editor.p5js.org/codingtrain/sketches/pLW3_PNDM p5.js Web Editor Sketches: 🕹️ Monty Hall: https://editor.p5js.org
From playlist Coding Challenges
How Games Twist Probability - Extra Credits Gaming
--- To learn more about Brilliant, go to https://brilliant.org/ExtraCredits/ and sign up for free. The first 200 people that go to that link will get 20% off the annual Premium subscription! --- Probability! A cornerstone for the design of any game. It can build excitement and suspense bu
From playlist Extra Credits: Game Design
Monty Hall Problem (extended math version)
Shorter version at: http://youtu.be/4Lb-6rxZxx0 And more: http://bit.ly/MontyHallProb This video features Lisa Goldberg, an adjunct professor in the Department of Statistics at University of California, Berkeley. Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.fac
From playlist Monty Hall Problem on Numberphile
Monty Hall Problem - Numberphile
Extended math version: http://youtu.be/ugbWqWCcxrg?t=2m32s A version for Dummies: https://youtu.be/7u6kFlWZOWg More links & stuff in full description below ↓↓↓ This video features Lisa Goldberg, an adjunct professor in the Department of Statistics at University of California, Berkeley. S
From playlist Monty Hall Problem on Numberphile