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 with no guarantee
There 's an 80% chance a ball is in a chest of drawers with 4 drawers.
If we open 3 and find they're empty ,what is the probability it s in the 4th (all drawers have an identical chance of having the ...
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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 ...
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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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Advice on optimizing an objective with many potential cases to track
I am analysing a game based on an extension of the Monty Hall problem and have come across an optimization problem that is just not clicking. I do not currently understand fully whether I should be ...
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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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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 ...
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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 ...
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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 ...
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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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