Questions tagged [monty-hall]

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

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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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Maybe a variation on the Monty Hall problem?

I have the following conundrum. I am given three Hot Dogs, one is bitten on both sides, one is bitten on one side and one is not bitten at all. I choose one at random and I see one end is not bitten. ...
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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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Monty Hall problem with biased door selection probabilities

I have the same question as here: Monty Hall problem with biased door selection probability Not sure what's wrong with this logic: Call $S$ the event of winning when I switch. Call $M_i$ the event ...
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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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Monty Hall Problem Where the Contestant Chooses Whether to Open Door [closed]

I am introducing two new rules to the Monty Hall problem: The Contestant chooses whether to open the door or not The door is opened randomly If the randomly door opened contains the money, the ...
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Reverse monty hall problem probability?

So I understand the monty hall problem fine but not the reverse. Premise of question: As I was watching a show on youtube there were 3 people eating burritos and one had a bad filling and one of the ...
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Monty hall intuition behind mistake

I'm working through a simple modification of the Monty hall problem from a homework for stat110 course problem 1b. Its basically the standard monty hall setup except that if Monty has a choice ...
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Does the Monty Hall problem occur on this situation?

Lets say, I have the following situation: I know, that an alarm will go on on a certain day. It will go on on any day from Monday to Sunday. On the week before, I know that the possibility is ...
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What is the probability that I will be one of the two winners out of 3 candidates?

I am one of the three candidates for an award given to 2 people. Am I right in thinking that My chances of winning an award is 2/3? Because if so, the other two also has 2/3 chances of winning and ...
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Extension of Monty Hall problem

I'm solving a single-choice question in the exam. The question has $4$ options: A,B,C,D. These are my steps: $1$. I didn't understand any choice of the four, so I randomly selected one: A. $2$. ...
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Monty Hall Extended To Two People

Person One enters the Monty Hall problem as usual with usual rules. Of the three doors A, B and C, One chooses B, Monty opens C (goat) and One switches to A calculating that the probability of a car ...
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Monty Hall Problem simulation gives weird answers

I tried to simulate the Monty Hall problem in Python, and ended up with 66% probability after a few attempts. However, the first incorrect attempts were more interesting, as they consistently gave a ...
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Monty Hall Problem-Probability Paradox

I just learned about the Monty Hall Problem and it seemed pretty much amazing to me.I am just a bit confused with it. So,according to the problem we are on a game show, and we are given the choice of ...
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Is this a Monty Hall Problem?

I asked the following question on an exam and want to verify I have the correct answer before marking it. “Your friend has three laptops that he wants to get rid of. He offers one of them to you. He ...
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Does Monty Hall Problem have any effect on an equation with multiple choices? [closed]

I am having a discussion with someone that insists the Monty Hall Problem would improve the probability of guessing the correct door. However, the circumstances are different. You have four doors. ...
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Probability of a given name be picked

Had a probability discussion about the following context: 10 names were put in a box. 2 names will be picked up randomly from it. What's the probability of a given specific name be picked? My ...
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Where have I gone wrong in this four door Monty Hall Problem?

Consider the classic Monty Hall Problem, but with four doors, labelled A, B, C, and D. I want to calculate the probability of winning with the strategy "choose, switch, stick". I'm struggling to get ...
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Monty Hall Problem involving 5 doors and probability tree [duplicate]

I recently came across a Monty Hall problem involving 5 doors. You are participating in a contest. There is one car behind five doors. After you select a door, the host will open three of the four ...
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Monty Hall problem: If contestant knows the door with goat…

I need to know the probability of this variation of the problem. Suppose that the contestant is a psychic and in some way he/she knows one and only one door with a goat. *The psychic can't know the ...
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Monty Hall Problem. If contestant choose door with goat and host reveal it…

I need to confirm this scenario. 1 - The contestant picks a door with a goat behind it. 2 - The host opens this door and reveals the goat. 3 - The host gives the contestant the chance to pick a new ...
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Monty Hall with 4 Doors Solution

I am trying to analyze a Monty Hall question with four doors (3 goats, 1 car) just so I can then apply the problem with n doors. I applied Bayes' theorem, calculated the probabilities and am trying ...
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Monty Hall Problem - Strategy that maximizes chances of winning the prize

On a game show, there are three doors, behind one of which is a prize. I choose a door and the host opens one of the other doors that has no prize behind it. I get to switch my door choice if I wish. ...
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In the basic Monty Hall problem, why not the probability are 50-50? [duplicate]

When reading the book of (Chapman & Hall_CRC Texts in Statistical Science) Joseph K. Blitzstein-Introduction to Probability Chapter 2. I have great puzzles about the second last paragraph. ...
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How does the knowledge of one's preference for A over B affect the probability of one's preference for C over B if one's preference is transitive?

Suppose you know someone has preferences between the three pizza toppings pepperoni, olives and mushrooms. If you are told that they prefer pepperoni over olives then what is the probability that ...
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Why's the probability of the unchosen doors' containing the prize reduced to the unopened door?

I understand, and ask not about, how to prove that you ought switch. Let $\Pr(✘)$ = probability that the unchosen doors have the prize (I chose the X mark to signify that you chose wrongly). Please ...
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Con-artist Monty Hall (Generalized)

For: d($t_a$) doors (not already picked or opened at time $t_a$ ), $c_{tot}$ cars (initially), p($t_b$) picks (which depends on d($t_b$) == doors available at time of choosing picks), o($t_c$) ...