Questions tagged [monty-hall]

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

(From Wikipedia)

The Monty Hall problem is a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990:

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, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Vos Savant's response was that the contestant should switch to the other door.

This solution is counterintuitive to many people, sparking a neverending debate whether one should switch or not (hint: one should).

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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 each question? At this point it seems logical…
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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, say No. 1, and the host, who knows what's behind the…
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Can there be generalization of Monty Hall Problem?

Monty Hall problem basically is: there are three doors, behind one of these doors is a brand new car, and behind the other two are goats, one picks a door that one thinks has a car behind, then the host opens one of the doors one didn't pick to…
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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 a car. After you make your choice, $33$ other…
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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 have chosen the door, Monty deliberately reveals one…
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Alternative Monty Hall Problem

So the typical set up for Monty Hall problem, there are 3 doors where 2 have goats and 1 has a car. I, the contestant, get to randomly guess a door looking to get the one with the car, after this the host will open a door that will always be a goat.…
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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 Who wants to be a Millionaire? when using the 50/50…
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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 three doors: Behind one of them is a car and…
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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 there is a car (which you want), and behind the…
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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 $1$ of $3$ doors. $3 \times 3 \times 3 = 27$ possible…
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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 answers that are wrong! And it happens that none…
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Yet Another Monty Hall Question - Please advise if alternative scenario proves the same principle

Okay, I'm very embarrassed that there are already 71 questions (based on search of "monty hall") and I'm going to post another one. I read the first 5 before succumbing to choice-overload. I'll try to keep this short and sweet. A host and…
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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 involved, as their probabilities seem to be…
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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
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Sleeping beauty problem and Monty Hall paradox

I read this argument on the internet about how the solution to the sleeping beauty problem is $\frac{1}{3}$: All these events are equally likely in the experiment : Coin landed Heads, it's Monday and Beauty is awake Coin landed Heads, it's Tuesday…
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