Questions tagged [monty-hall]

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

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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 ...
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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 $2$...
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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 ...
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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 ...
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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 ...
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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, ...
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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. ...
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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 ...
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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 ...
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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 ...
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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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An elegant solution to the classic Monty Hall problem.

Think of the game as drawing a ball, blindfolded, from a box, which contains 1 white ball and 2 black balls, except that every time after you pick a ball, a black ball will be thrown away by the host, ...
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Monty hall with $n$ doors and Monty opening $m$ doors

In Monty Hall problem generalized to $n$ doors, the Monty hall's problem was generalized to $n$ doors with Monty opening $m$ of them, where $m < n - 1$. The probability of winning by switching is $\...
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Monty Hall Problem + dice - Why does the probability of whining the car raises after switching doors? [closed]

I'm trying to understand the Monty Hall problem. When the contestant switches the door the probability of them winning a car is higher than if they continued with their first choice. Why would the ...
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I understand the intuition of the Monty hall problem, I do not understand the math

Take the famous Monty Hall problem. There are three doors, one has a prize. If you pick the door with a goat, he reveals the other door with the goat. If you picks the door with the car, he randomizes ...
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Monty Hall: What is the "unconditional probability of success" and "conditional probability of success"?

Can someone explain the highlighted paragraph from Blitzstein, Introduction to Probability (2019 2 edn), p 69? I'm not understanding the subtlety the author is trying to get at. What is the "...
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Monty Hall Problem with Multiple Players?

I understand the common Monty Hall Problem and why switching provides a 2/3 chance of winning, but I'm having trouble wrapping my head around how the probabilities work when multiple players are ...
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What is wrong with my solution to the Monty Hall problem?

I'm trying to develop an intuitive sense of why the suggestion of the Monty Hall problem is that you should switch doors when an informed host opens one of the two dummy doors. So, I'm trying to think ...
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Does Monty Hall apply here?

Alice picks a card from a deck of cards. Bob guesses what her card is. Say Bob guesses the King of Hearts. Alice says her card is a heart, and gives Bob the option to keep his current guess or to ...
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Monty Hall Problem - what is the probability space for the problem, and a question on $\sigma$-algebras generated by events?

So we have the following problem where we have 3 doors, 1 has a car behind it and 2 don't: i) We first choose door 1 ii) Monty opens one of the other doors which he knows for certain doesn't have a ...
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Three player combinatorial game - minimizing communication between Alice and Bob

Consider the following game between three parties: Alice, Bob and a Referee. The game starts with $n$ closed boxes. For some fixed $k<n$ known to all parties, the Referee freely chooses $k$ ...
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Discrepancy between probability from participant perspective and probability from game perspective in Monty Hall problem

If we calculate Monty Hall problem from individual point of view, we obtain the following options ...
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Monty Hall problem but for 1000 doors (by Bayes theorem)

I know how to prove this statement by Bayes theorem when we have 3 doors with one car. But is it possible to solve this problem using Bayes theorem for 1000 doors? In case with 3 doors I considered 4 ...
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Can Monty Hall be applied to Among Us?

I came across a video (not sure if I'm allowed to post it because it had some kid was swearing due to the nature of the game's lobbies) where the guy claimed that you can apply Monty Hall to Among Us. ...
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Monty Hall problem five doors [duplicate]

Suppose you’re on a game show, and you’re given the choice of five doors: Behind one door is a car; behind the others, goats. You pick a door, and then the host, opens two of the doors, which ...
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Fallacy in conditional probability solution for the Monty Hall Problem

I know there are various established explanations for the problem. But here is my approach: Just to be specific, the exact problem is as follows: There are $3$ doors. Behind one of them is a car and ...
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Monty Hall's problem argument [duplicate]

Let us take 3 doors A, B, C. Now, let us say car is in A. Now if player selects A, host opens B, on switching player loses. If player selects A, host opens C, on switching player loses. If player ...
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How to solve monty hall with 5 doors using bayes theorem?

With 5 doors we get the following events. A: Probability of choosing a door with a car behind it: 1/5 ...
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Monty Hall Problem

Overall, I think I understand the Monty Hall problem, but there's one particular part that I either don't understand, or I don't agree with, and I'm hoping for an intuitive explanation why I'm wrong ...
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Problem similar to Monty Hall Problem [duplicate]

Let's say I get paid by my boss. There are 2 envelopes, A and B. I know for a fact that one envelope contains twice more money than the other one. 1) If I pick an envelope A, and the boss asks me if ...
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Probablilty - Monty Hall problem

A candidate chooses a door (which remains closed at first), so that he can win a car behind. Moderator opens n-2 other doors with goats. 2 doors remain closed. We consider the goat problem for n=5 ...
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The Monty Hall Three Door Puzzle [duplicate]

I was going through the Monty Hall Three Door Puzzle in "Discrete Mathematics and its Application" by Kenneth Rosen (5th Edition). While reading the excerpt from tbe book (given below) I could not ...
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Monty Hall Problem simulation - win lose rate doesn't seem to match the expected outcome [closed]

I created a simulation in Python for: A) A player who sticks with the chosen door B) A player who switches door after hosts opens a door without a price. For scenario A) I get 66% lose rate (33% win ...
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Monty Hall Problem - Host doesn't know confusion

I am given the variation of the Monty Hall problem, where the host does not know where the car/goats are. There are three doors labelled A, B and C. Let probability of choosing A, and the host ...
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Conditional probability VS A Intersection B

I recently came across the Monty Hall Problem. And while I get the gist of it, what I am having trouble understanding is this specific part of it. Say I pick door 1. Then the probabilities for the ...
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Monty Hall Game (audience selected to open a door at random)

The classic Monty Hall game is as follows: There are 3 doors. 1 door contains a prize. The other 2 doors do not. The prize has an equal chance of being randomly placed behind a given door. The ...
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Monty Hall Analogue

I am studying this variation of the Monte Hall problem. There are three prizes as before (1 car and 2 goats). The host picks two out of the three items for you at random. The host then views both ...
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Bill Gates Investment Problem

Bill Gates will invest in only one of 5 companies: $C_1$, $C_2$, $C_3$, $C_4$ or $C_5$. I will make a lot of money if I invest in the same company. I decide to invest in company $C_1$ and I inform ...
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Why are the two probabilities in the Monty Hall problem dependent on each other?

Like most people, one of the first things I did after ringing in the new year was get into a discussion about the Monty Hall problem. Past discussions typically amounted to the other person saying, "...
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In the Monty Hall problem, why isn't Pr(I switch and win| Monty opens door 2) = 1/2?

I have this same question. What's wrong with my logic? Call $S$ the event of winning when I switch. Call $M_i$ the event Monty opens door $i$. WLOG I choose door 1. $P(S|M_2) = P(S|M_2,D_1)P(D_1) + P(...
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Monty Hall Problem - $4$ doors where you pick one by one

I encountered the problem of Monty Hall Problem with $4$ doors ($3$ doors $1$ goat). However in this variation you pick an initial door. Monty reveals one goat. Thereafter you either switch or stay - ...
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Monty Hall variation, where goats are followed by random doors

3 doors, 2 of which have undesirables behind them, 1 of which has a prize behind it. The items are randomly distributed. Monty's behaviour: If you first choose the door with the prize, then Monty ...
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Help to understand the Monty Hall problem formally

The concept of the problem is well known. So, in short for not to waste your time guys: $A$ - behind the door #1 there's a car $B$ - Monty opens the door #3 $C$ - behind the door #2 there's a car $P(...
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Modified Monty Hall problem: Probability of winning the car GIVEN that you change the door

The probability of the prize being behind each door is .5, .3, .2 respectively. The participant opens door one. But the problem states that the fact that the contestant does not choose the original ...
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