# 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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1 vote
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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 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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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(...