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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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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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2answers
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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: 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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3answers
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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($t_c$) ...
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2answers
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Monty Hall: What's wrong with my approach

Let us say we have n boxes, and one car. The probability that one of them might have a car = p and each box is equally likely to have a car, therefore the change that a single box has car = p/n ...
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What is the mistake in the following contradiction to the solution of the Monty Hall problem?

Let us say in a game show there are three doors - 1,2 and 3 - behind which are hidden 1 special prize and 2 useless objects. The host knows which door leads to which object. Let there be two ...
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Monty Hall problem with coin flip

Before each show, Monty secretly flips a coin with probability p of Heads. If the coin lands Heads, Monty resolves to open a goat door (with equal probabilities if there is a choice). Otherwise, ...
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Monty Hall Problem. If host open door before the player choose a door.

What happened if in the Monty Hall problem the host open a door with goat (he knows the door without prize) before the player pick a door. There will be 1/2 of probability of success or 2/3 as the ...
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1answer
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How often will two random integers between one and three (boundary inclusive) be the same?

Assuming the answer is one out of three? And, also, would this be a good distillation of how to understand the "Monty Hall" problem?
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Monty Hall Problem - Probabilities of the final choice [closed]

Is the probability of swapping to the only other available door the same as the probability of the result of a coin flip to determine your last decision? For example, Heads you stay on the current ...
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3answers
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How to solve the Monty Hall problem using Bayes Theorem

I've recently come across the Monty hall problem and while the reasoning behind switching doors makes sense intuitively to me I can't seem to understand the maths behind it. I've seen many proofs ...
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A confusion about the Monty Hall problem [duplicate]

After reading the other question about the Monty Hall problem, and seeing the solution of it, before giving my perspective to the question, I would like to point out that, to explain the possible ...
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Does Monty Hall logic apply to this real world situation?

I recently posted a tweet claiming I had encountered a real life Monty Hall dilemma. Based on the resulting discussion, I'm not sure I have. The Scenario I have 3 tacos (A,B,C) where tacos A and C ...
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5answers
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A reverse Monty Hall problem

A protagonist is set with four cups, three containing water and one containing poison and proceeds to drink three cups. (yes, the setup is similar to another question. However, the question is unique) ...
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3answers
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How does the Monty Hall Problem work? [duplicate]

So I was reading a few maths problems and I stumbled upon the Monty Hall problem. If you are not familiar with the Monty Hall problem it goes something like this: You are on a game show (with the ...
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How to model and solve the variant of Monty Hall problem in which the host opens a door randomly?

The Monty Hall problem (wiki) is described as follows: 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,...
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Monty Hall Variant Game

There are three doors, behind each is either a car, or a goat. Unlike the original Monty Hall problem, there are 8, equally likely possibilites for the setup of the doors. The possibility sample ...
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2answers
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Bertrand's Box Paradox Generalized

Original Problem There are three boxes, each with a different combination of gold and silver bars in them: One has two gold bars, one has a gold and a silver bar, and one has two silver bars. If a ...
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Monty Hall problem generalized to $n$ doors

Generalize the Monty Hall problem where there are $n \geq 3$ doors, of which Monty opens $m$ goat doors, with $1 \leq m \leq n$.Original Monty Hall Problem: There are $3$ doors, behind one of which ...
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1answer
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Another Monty Hall problem

You are playing a game in which there are four doors, behind one of them there is a car and behind the other 3, there are goats. The car is equally likely to be behind any door. The game show host ...
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1answer
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Monty Hall problem with biased door selection probability

Consider the Monty Hall problem, except that Monty enjoys opening Door 2 more than he enjoys opening Door 3, and if he has a choice between opening these two doors, he opens Door 2 with probability $p$...
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Am I wrong about the Monty Hall Problem?

First off, I don't think its 50/50 always. That's not what this is about. I know that simulations show that if Monty randomly picks a goat, it IS 50/50. I always thought I understood why this was, ...
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Is this informal solution to the Monthy Hall problem wrong? And why?

I recently opened my high school book about probability and statistics and I found an informal solution to the Monthy Hall problem. I translate it here: "Let's suppose that the first door chosen by ...
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1answer
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Monty Hall problem with 7 doors [duplicate]

According to the Monty Hall Problem, I select a door, say door number $1$. Monty then opens $3$ of the remaining $6$ doors that do not contain the prize. The question is should I switch. Note that ...
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2answers
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Monty Hall Problem With Uneven Door Probabilities

In the conventional Monty Hall problem it is assumed that the probability of the car being placed behind any of the three doors is the same (namely, $\frac{1}{3}$). (In other words, the host has no ...
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Monty Hall Problem : Alternate View

Considering we all know about Monty Hall Problem of $2$ Goats and $1$ Car. Also, the solution of the probability $2/3$ concentrating on a single door. Now, an alternate approach can be as follows: ...
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Variant on a Large-Scale Monty Hall Problem

I finally figured out the logic behind the Monty Hall problem and why it works the other day. Reflecting on other explanations I've seen, I hit upon the commonly provided one where instead of 3 doors ...
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Monty Hall Problem with twist

I have a version of the Monty Hall Problem with a slight twist. Classic Setup Suppose there are 3 doors to choose from. You have to get the correct door. Once you choose one door, one of the wrong ...
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1answer
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Monty Hall Pt. 2?

This problem is from Introduction to Probability by Blitzstein and Hwang (Chapter 2, exercise 41). You are the contestant on the Monty Hall show. Monty is trying out a new version of his game, ...
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2answers
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monty hall multiple prizes

Really surprised I didn't see this already posted on math SE...(as far as I can tell) I understand the N door, k-revealed Monty Hall extension: Monty hall problem extended. The solution is to switch ...
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Is this a modified Monty Hall problem (numbered doors)?

On a job interview, I got this question: Monty placed a car and two goats behind three identical doors (and the things do not move during the game). You receive the prize which is behind the door ...
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Monty hall problem probability 2/6?

For the Monty hall problem, with 3 doors, two of which have sheep and 1 has a car. I calculated the probability of getting the car if you swap being 2/6 instead of 2/3. I have drawn this tree diagram ...
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Is there a word for taking a statistical model, and working backwards to the algebraic proof?

As an example, I'm trying to work backwards from the statistics generated from the Monty Hall Problem and figure out the variables and their relation to each other. The specifics of the Monty Hall ...
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What is the best algebraic proof of the Monty Hall problem (e.g.: xor(a xor { C < B or B < C }) = 1)

I want to look at the Monty Hall problem as a way of measuring the host's involvement in the game. Namely: The game show host's knowledge and action results in a change of the outcome of the game ...
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Alternative analysis of the Monty Hall problem

The widely accepted answer for the Monty Hall problem is that it is better for a contestant to switch doors because there is a $\frac23$ probability he picked the door with a goat behind it the first ...
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Monty Hall Problem - Extended

So, take the usual Monty Hall setting - 3 doors and one car, 2 goats. I can reveal a door once you've chosen yours. Then extend it to a situation, where,if you SWITCH, the door you switched from is ...
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Question about Monty Hall if you already knew a bad door beforehand

So the setup of the scenario here is exactly the traditional Monty Hall problem. Except, before the game starts, you decide to cheat and open a door and it happens to be a goat. Before you can peek at ...
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Probability about switching choices

This question is similar to the Monty Hall problem, but this problem I don't understand: There are $99$ doors where $33$ doors have cars and $66$ have goats, and you can only choose one door to win ...
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1answer
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Monty hall problem with uneven probability opening door 2 and conditioning on it

I was doing the Monty hall question on harvard's stat 110 strategic pratice 3 Question 1 (b) https://projects.iq.harvard.edu/files/stat110/files/strategic_practice_and_homework_3.pdf so basically ...
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monty hall induction

Recently, I learned how to solve the Monty hall Problem through Bayes' theorem. Since this is a direct way of proof, I was interested whether the problem can be solved by mathematical induction. ...