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Questions tagged [monty-hall]

The Monty Hall problem is a probability puzzle with a solution that is counterintuitive to many.

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is my solution correct to a Monty hall variation with 4 doors?

Problem: You've participated in a new type of "Who Wants to Be a Millionaire?" quiz. The last question worth 1,000,000 euros is remaining. The question is difficult, and you have no idea ...
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Are unconditional probability and conditional probability method necessary to generate the same result?

mcs.pdf shows 2 methods to calculate the probability of "switch wins" for Monty Hall problem. unconditional probability (See Figure 17.5): So we have the probability $\frac{1}{9}\cdot 6=\...
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Combating a specific argument against the Monty Hall problem .

So to get started , I make it clear that I do know how the Monty Hall problem works and although I had my good share of problems understanding it in the past , I did manage to come to terms with it on ...
Mike Billings's user avatar
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Monty Hall problem - doesn't it matter that you know from the start that a goat will be revealed with 100% certainty?

I know that the Monty Hall problem is old news. However, I can't get this out of my head and I am looking forward to your thoughts about it. If the rules of the game are known from the beginning, ...
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Why isn't the denominator in bayes rule always one

So, I thought I kind of understood Bayes and total probability, but I see now I am not clear on the calculation and which information to take in. I read an article that was using the Monty Hall ...
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(SOLVED) Monty Hall: the number of unknowns decreases but probabilities stay the same?

I recently got an explanation of the Monty Hall problem and I thought I understood it but after giving it more thought, it still looks wrong. Instead of using goats and doors, the example used a 52-...
moumous87's user avatar
2 votes
3 answers
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Monty Hall Problem, but the contestant opens the door.

In The Monty Hall Problem, suppose there are three doors A, B, and C. Suppose the contestant chooses the first door A. The variation comes here, suppose that the contestant now has the option to open ...
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Monty Hall Uneven Door Probabilities - Conditional Door Opening Probability

I've been reading about this variation of the Monty Hall problem described in "The Monty Hall Problem" by Jason Rosenhouse. Specifically "3.10 - What If the Car Is Not Placed Randomly&...
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Werewolves vs Town Jailer – does this work like the Monty Hall problem?

In the game of Werewolf (also known as Mafia), a small group of werewolves is hiding in a larger group of villagers. During the “night” phase of the game, the werewolves choose one villager to kill. ...
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Monty Hall Dilemma with conditional probability

The initial probability of each door being the winner is 0.1 for door 1, 0.2 for door 2, 0.3 for door 3, and 0.4 for door 4. The formula for solving each conditional probability involves an ...
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Why is the probability of host opening door $3$ in Monty Hall $1 \over 3$?

I have been told that the probability of the host opening door $3$ in the Monty Hall problem is $1 \over 3$ (a priori, given no other information about what has transpired in the game), but when I ...
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How is it better to switch in the Monty Hall Problem? [duplicate]

I'm not a mathematician so I'm probably getting something wrong here, but no matter how I think about it I can't accept that it is necessarily better to switch. Here is my best attempt at a proof: ...
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A new monty hall problem

could someone help me to solve this question with the use of bayes theorem? What would be the optimal strategy and its probability to win an item of the greatest value if the Monty Hall problem was ...
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Spin on Monty Hall

Coming from Blitzstein's book, here is a paraphrased version of the question. Consider a version of Monty Hall where there can be more than one car, and each of the 3 doors independently have ...
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In case player chooses winning door in Monty Hall, Do we need to consider reveling goat 1 and goat 2 as same choice or different choice in solution?

While solving Monty Hall Problem, In possible positions/choice table, There is a case where player initially chooses car (winning) position and host has to reveal either goat 1 position or goat 2 ...
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Monty Hall Style bag of marbles problem

Inspired by question $7a$ on the Euclid Maths competition $2023$, I have been stuck thinking about the following simplified version. A bag contains $2$ blue marbles and $1$ red marble. You remove one ...
Vincent Cattoni's user avatar
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Monty hall is allowed to show a car

I am trying to solve the Monty Hall Problem with $3$ doors ($2$ goats, $1$ prize) with a simulation of the rules You initially pick a door randomly from the 3 possible doors. Monty hall does not know ...
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Monty Hall problem: Is the probability to win by switching $2/3$ even if we don't know the host's behavior?

Preview Some of the confusion with the Monty Hall problem comes because it is not always stated that the host must always reveal a goat from the two doors that the player did not pick and offer the ...
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Help understanding logic in a proof in the paper "Monty Hall game: a host with limited budget"

I am trying to follow the logic in a proof of a lemma in the paper named in the question above. (It focuses on a version of the Monty Hall problem and can be found here, and a previous question I ...
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1 answer
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Probability - a variation of the Monty Hall problem

There are 6 doors in the game. Behind two (different) doors chosen at random is a prize. Alice chose one of the doors, marked x. Moderator Bob randomly opens one of the other doors that does not ...
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Explaining the Monty Hall problem

Explaining the rules of the game: There are three doors. Only one contains the prize. You choose one door first, then Monty Hall opens one of the other two doors that doesn't have the prize. If there ...
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Extended Monty Hall Problem

This is not a duplicate of Extended Monty Hall Problem. Let the Extended Monty Hall problem. i.e., it is a game where there is $n$ doors and a car behind one, and only one, door. After the player ...
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Monty Hall Problem Trouble

This problem is from Introduction to Probability by Blitzstein and Hwang (Chapter 2, exercise 40) The ratings of Monty Hall's show have dropped slightly, and a panicking executive producer complains ...
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"Monty hall"-esque marble selection problem driving me insane

The quiz and explanation is from Brilliant.com course "Exposing Misconceptions". Summary of the problem: Two random coins are flipped and put in a bag(without changing orientation). One ...
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Understanding Monty Hall problem [closed]

I was reading the Wikipedia page for the solution to Monty Hall problem using Bayes' theorem. I am very confused about this part P(H3|X1) = 1/2 because this expression only depends on X1, not on any ...
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Monty Hall Problem Wrong Reasoning: By Considering All Possibilities

Monty Hall Problem: https://en.wikipedia.org/wiki/Monty_Hall_problem Here is a wrong reasoning. I am unable to find the flaw in it. Given below I have attached three images which give us the three ...
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Looking for a good explanation (or proof?) about the Monty Hall problem

The Monty Hall problem (https://en.wikipedia.org/wiki/Monty_Hall_problem) is about a game show in which the player is given the choice of three doors. There's a car behind one of the doors and a goat ...
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I've found this problem on transpositions absolutely intractable.

A University bike shed contains n cubicles in a row. Each cubicle stores one bicycle. One morning, Professor Ponte places his bicycle in one of the cubicles. At night Priyanka attempts to steal his ...
Indianimperialist123's user avatar
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Monty's choice of door to open when the car is behind the door initially chosen by the contestant

In the Monty Hall game, suppose that whenever the car is behind the door initially chosen by the contestant (so that Monty Hall may open either one of the remaining two doors), he chooses to open the ...
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Another probability game

Here is a contrived game, that there could be some benefit for solving. I hope it will turn out somehow like the Monty Hall problem. A gameshow. First here is the simpler game. A contestant spins a ...
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Is the following coin-toss problem analogous to Monty-Hall?

Suppose you flip a coin three times. What's the probability that all three flips result in the same outcome, i.e., all three heads or all three tails? There seem to be two solutions... There are the ...
John Forkosh's user avatar
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Does the Monty Hall problem imply one should always change choice after receiving new information?

In the Monty Hall problem the player can choose one of three doors. One hides a valuable reward, the others, goats. Once the player chooses a door, one of the other doors is revealed to have a goat ...
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What variable am I missing in order to partition the Monty Hall problem into its fundamental outcomes?

Here are the basic outcomes I have come up with to describe the Monty Hall problem... Player selects Door A, Monty opens Door A, Player stays, Car is behind Door A = Impossible Player selects Door A, ...
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I performed an experiment similar to see if switching really works in the monty hall problem, It didn't.

I recently learnt about the Monty Hall problem. Theory says you should always switch since probability of winning then is twice. But I feel why won't probability be redistributed and be half for each ...
Anurag Mishra's user avatar
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1 answer
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Variant on the Monty Hall Problem ($4$ Doors, $2$ Prizes)

I had the following question as part of a Finance course I'm doing. I don't struggle too much with Monty Hall problems in which there are $3$ doors, but this one with $4$ doors ($2$ with Prizes and $2$...
Daniel Hardej's user avatar
2 votes
1 answer
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A generalized Monty Hall problem

I am considering a generalized Monty Hall problem. Let $D$ be a set of doors, $|D| \geq 2$. A car is behind one door, and goats are behind all the others. Instead of having to choose a single door as ...
Usagi's user avatar
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What is the probability of your next choice that make your choices uniformly distributed

Given an #n of balls. you are only allowed to pick between two balls at a time with a probability $P_{i}=0.5$ with i being the number of the ball. For example: you're presented with a black ball and a ...
Dev chimp's user avatar
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What are the odds of picking one outcome out of three, if you have two attempts and the one you pick is removed from the pool?

Edited for (hopefully) clarity. There are three cards on the table facedown, two with the [o] symbol and one with [x]. You must find [x] to "win" and you have two attempts. If you do not ...
Kard Nails's user avatar
3 votes
2 answers
176 views

Two people Monty Hall paradox

We're on a game show, and we have to select between three doors, one of which has a Lamborghini behind it while the others have goats. After we've decided, the host opens one of the other two doors, ...
The One's user avatar
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3 answers
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Monty Hall Change in Problem Suggestion

So, Let's say we have three doors and three guests in our show. A car is behind one door. The other two doors have goats . Please note.. I am not asking about the original Monty Hall problem here. ...
Nidal J's user avatar
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1 answer
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Monty Hall Variant a priori probability of winning by whiching when Monty has preference for door 2

I am working on the below problem (38) from Joe Blitzsteins Introduction to Probability and I accidently answered a slighty different question, which it would be great to check the answer to: Question:...
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Standard Monty Hall problem: proof that switching is optimal?

I have a model of the Monty Hall problem that as far as I know is standard: three doors, the contestant chooses one at random, then if Monty has a choice (i.e., the contestant has chosen the door with ...
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Explaining Monty Hall problem by Bayes' theorem

The Monty Hall problem is the famous puzzle that, in a game of choosing the right box containing the treasure, one should switch to another box when told that one of the unchosen ones is empty. My ...
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Probability of random draws and whether switching makes a difference or not

We have a game and I can place my character in one of 4 spots, each corresponding to 1 tile (so we have spots 1 through 4 and we have 4 tiles numbered 1 through 4). We will randomly draw one, put it ...
Joao Pedro's user avatar
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Solving the Monty Hall problem using Bayes Theorem

Let $A_{i}$ be the event "the prize is in th $i$ - th door". Let's consider $P(A_{1} | A_{2}^c)$, that is, the probability that the prize is in the first door, given that it is not in the ...
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Monty Hall Variation 2

It is the same scenario as Monty Hall, except this time the contestant states which curtain he does not want, let's say C1. One of the remaining 2 curtains are opened to reveal a goat, say C2. To win ...
Paul Barber's user avatar
1 vote
1 answer
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Probability of Ace of Spades in Monty Hall Like Scenario

I select a card at random from a standard deck of playing cards. The probability of this card being the Ace of Spades is 1/52. From the remaining cards, someone turns over all but one, and none of ...
Robin Andrews's user avatar
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$N$ doors Monty hall type problem

In Peter office there are $N$ doors. Behind each door except one hides a doll. Lucy know what is behind each door while Peter does not. Peter has to select a door and wins if there is no doll behind ...
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Monty Hall Problem with unknown probabilities

Does someone know a solution to the following generalization of the Monty Hall Problem: The Problem: Assume you are on Let's Make a Deal and are presented with the regular dilemma of the Monty Hall ...
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Monty Hall problem with $n$ doors and $m$ cars

I have a problem regarding a modified Monty Hall problem. In this monty hall problem we have $n$ doors and $m$ cars, where $n ≥ 5$ and $1 ≤ m ≤ n − 3$. The rule of the game is also changed: you choose ...
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