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

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Monty Hall Problem Intuition

I was thinking about the Monty Hall problem and I thought of a possible intuitive explanation: You choose a door. Monty gives you the option of sticking with your original choice or instead ...
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Probability: A deck split into piles

I have a deck of cards labeled $1, 2, \ldots, 9$. I give them a good shuffle and split them into $3$ piles, each with $3$ cards. Let's call these piles $A, B, C$. I draw the top card from pile $A$ ...
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Monty Hall Variation: Choosing 2 Doors

I'm learning about the Monty Hall problem, and found a question which has confused me: Consider the following four-door Monty Hall problem: Step 1: you choose one door such as door 1. Step 2:...
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Monty Hall Problem extended

After seeing the popularity of the standard $3$ door problem, Monty thought to put a twist in the story. There are $N$ doors, $1$ car, $N-1$ goats. We need to choose any one of the doors. After we ...
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Can the Monty Hall paradox be explained by Berkson's paradox?

I just learned about Berkson's paradox, which says that if $A$ and $B$ are independent, then $P(A\mid B,A\cup B) < P(A\mid A\cup B)$ (knowing that $A$ or $B$ occur creates a negative dependence on $...
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Could the Monty-Hall Problem be applied to multiple choice tests?

Given a multiple choice test where each question contains 4 possible answers, what would happen if before beginning the test (before reading the questions), someone were to make a random selection for ...
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Monty-Hall-Problem / Complete Tree of Possibilities [duplicate]

EDIT: I know that this is a trigger topic. I know there is a hell of posts out there. I don't need to be told, that I should switch, neither why. I want to know, what is wrong with those trees. If ...
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What's wrong with this equal probability solution for Monty Hall Problem?

I'm confused about why we should change door in the Monty Hall Problem, when thinking from a different perspective gives me equal probability. Think about this first: if we have two doors, and one ...
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Why does the Monty Hall problem not apply when the contestant picks the second door?

So, we all know the Monty Hall problem. Where there are 3 doors with one winning door. The contestant picks a door, then the host removes a non-winning door from the remaining two. Then the ...
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Why is my Monty Hall answer wrong using Bayes Rule?

The Monty Hall problem is described this way: 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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Translation between Monty Hall and Gold bars problem

When I read this question (problem restated below), and the first comment, I was drawn to the great similarities between this problem and the Monty Hall problem (asking for the winning probability if ...
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Monty Hall Problem: Reasoning Behind the Logic [duplicate]

I watched Lecture 18: Probability Introduction from the MIT OpenCourseWare where the lecturer talks about the Monty Hall problem. He draws the decision tree and we find that actually you have a 2/3 ...
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A slight variant of the Monty Hall Problem.

Suppose that there are 4 doors having 2 cars and 2 goats. You arbitrarily choose a door, then Monty shows a door with a goat. What is the probability of getting a car if you switch. Apparently the ...
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Unknown Card Monty Hall

I'm trying to understand this problem better and whether or not it is defined as a variant of the classic Monty Hall problem. Let's say there are X cards in a deck of cards. A copy of this deck of ...
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Does a “guarantee” change probability? (variation of three card problem)

This is a variation of a probability question (Bertrand's box, or the three card / two color question) that's been asked many times before. However, this question relates specifically as to whether or ...
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Another Monty Hall Question

I still do not believe the "correct" solution to the Monty Hall Problem. Here is my reasoning: The player can pick from $1$ of $3$ doors. The prize can be behind $1$ of $3$ doors. Monty will open $1$ ...
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In the Monty Hall problem, is it correct to think the probabilities of the two unchosen doors as shifting?

I was explaining the Monty Hall problem to someone thus: You have three doors, and you pick one, giving you a $1/3$ chance of being right. The presenter opens one of the other two doors, knowing ...
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Monty Hall Problem with Five Doors

My math class went over the original Monty Hall problem a few days ago, then looked at a related question where the number of doors was increased to five. There was a struggle to figure out what the ...
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Monty Hall problem extended with expectations i.e. prior probabilities

I am fascinated by the Monty Hall problem and its variants such as N-doors version here. Now suppose expectations. How does the Monty Hall problem changes with expectations? Simple example ...
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Variation of Monty Hall problem [duplicate]

On a game show, the Monty Hall problem is being played. The contestant is told to pick a door, and he does, but just before being able to tell the host which door he picked, one of the doors that the ...
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Monty Hall/Bayes' Theorem conflict?

Given the Monty Hall problem: Assuming Player chooses door A and Monty opens door B, what is the probability that the car is behind door C? The following calculation can be found in many places in ...
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Gambler's Fallacy, or Monty Hall Problem?

Assume a case where there are 30 doors. 29 have goats, and 1 has a car. You begin to chose doors one by one until there are only two doors left. All the doors you have chosen have been goats, leaving ...
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The Monty Hall Problem: 2 contrasting answers.

In the Monty Hall Problem, there are three doors. Let's take two scenarios. In both the host reveals that there is a goat behind door number two. In the first scenario, I choose the first door. ...
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Monty Hall Problem Solve Using Detailed Algebra

I have been searching the monty hall problem for two days now and I generally understand it but I am having a very hard time solving the monty hall problem using Bayes's theory. I do not know what ...
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50/50 Joker of “Who wants to be a Millionaire” - A “Monty Hall Problem” variation?

So the Monty Hall Problem itself is widely known and understood. Nonetheless, a friend of mine and I were wondering whether the the same strategy could affectively be applied by a participant of ...
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Monty hall - random goat reveal

This is a variation of the famous Monty Hall problem. I assume you know the usual setup. Here, the host behaves a bit different: The host knows what lies behind the doors, and (before the player'...
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3 Pancakes Problem [duplicate]

You have 3 pancakes in a stack. 1 is burned on both sides, 1 burned on 1 side, 1 burned on no sides. What is P(burned on other side — burned on the top)? Intuition (which is always suspect in ...
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Help with monty hall problem

I'm having trouble understanding something about the monty hall problem. If monty opened one door before you arrives, then you would have a 50/50 chance, whichever door you picked, because there are ...
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Monty hall problem extended.

I just learned about the Monty Hall problem and found it quite amazing. So I thought about extending the problem a bit to understand more about it. In this modification of the Monty Hall Problem, ...
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Great Monty Hall application in real life?

Suppose you are doing a multiple choice question with 4 different answers you have no ideas about. You mentally choose one (say A), and as you are about to write that down... you suddenly remember 2 ...
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Does The Monty Hall Problem Still Apply With Infinite Doors?

Here's been a bunch of questions on the Monty Hall problem, so I'll assume people know the basics. This answer helped clarify a few things for me, but talking with some colleagues yesterday, someone ...
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Cards Probability like Monty Hall Problem

During a certain game show, contestants are presented with a standard 52-card deck. If the contestant picks the Ace of Spades they win the grand prize. The contestant is asked to select a card and put ...
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Modified monty hall problem

Hello how to show the following You are given the choice of 3 doors. Behind one is a car and the other two are goats. You pick a door uniformly at random say 1, and Monty opens another door, say 3 ...
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What is the Nash Equilibrium of the Monty Hall Problem?

The Monty Hall problem or paradox is famous and well-studied. But what confused me about the description was an unstated assumption. Suppose you're on a game show, and you're given the choice of ...
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One variation of Monty Hall problem [closed]

Here once Monty has a choice to open any of two doors each containing a goat (i.e. when our initial choice is a car) then he chooses the rightmost one. We need to prove that here also the "overall" ...
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Monty Hall problem vs. roulette systems - how are they different?

So I got interested in the Monty Hall problem - I understand what it's about, but somehow I can't wrap my head around the idea of the final choice not being 50/50. More precisely: we all know (or ...
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Monty hall problem with leftmost goat selection.

We've all heard of the famous Monty Hall problem. However, what if Monty always picks the leftmost goat (and the player knows this)? Does this change the problem? I don't think it does because Monty ...
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Variation of the Monty Hall Problem.

Suppose instead of the normal Monty Hall scenario in which we have two empty doors and a car residing behind the third, we instead have three types of objects. One is a car, one is a hard drive, and ...
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Monty Hall Three-Door Puzzle

I have a doubt concerning a question about the Monty Hall Three-Door Puzzle, in probability. I found this problem in Rosen's "Discrete Mathematics and Its Applications". The Monty Hall Three-Door ...
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A variant of the Monty Hall problem

Everybody knows the famous Monty Hall problem; way too much ink has been spilled over it already. Let's take it as a given and consider the following variant of the problem that I thought up this ...
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Variation on the Monty Hall Problem

Many of us know the Monty Hall Problem But the other day I was asked a variation of this riddle. The answer of the original question is, of course, $ 66\% $ in favor of changing doors, but this is ...