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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Monty Hall - 1000 Exercises in Probability

The following problem is exercise 1.4.5(a) in One Thousand Exercises in Probability: 5. The Monty Hall problem: goats and cars. (a) Cruel fate has made you a contestant in a game show; you have to choose one of three doors. One conceals a new…
user144527
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Monty Hall problem again (from Grimmett and Stirzaker)

Grimmett and Stirzaker Exercise 1.4.5.2 In a game show you have to choose one of three doors. One conceals a car, 2 conceal goats. You choose a door but the door is not opened immediately. Instead the presenter opens another door, which reveals a…
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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 only 2 doors to pick from - right? So, what about…
Benubird
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Monty Hall vs. Card Example

In class, while illustrating the topic of conditional probability, my professor presented the following card example: You have 3 cards that have been randomly shuffled: card1, card2, and card3. One is an ace and the other two are non-aces. We are…
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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. This is another problem (but eventually it might be…
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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 a car) he chooses his door to open at random,…
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Monty Hall Analogue

I am studying this variation of the Monte Hall problem. There are three prizes as before (1 car and 2 goats). The host picks two out of the three items for you at random. The host then views both items and then shows you one of the items which is a…
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Does the Monty Hall problem occur on this situation?

Lets say, I have the following situation: I know, that an alarm will go on on a certain day. It will go on on any day from Monday to Sunday. On the week before, I know that the possibility is equal (1/7). My question: When it's Wednesday, two…
Myzel394
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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 contestant is given the option of switching doors. The…
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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 Puzzle: Suppose you are a game show contestant. You…
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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 just one goat door, and one car door. Now two…
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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 brought up the idea that as you increase the…
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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 two doors then Monty reveals another door where…
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Monty Hall Extended To Two People

Person One enters the Monty Hall problem as usual with usual rules. Of the three doors A, B and C, One chooses B, Monty opens C (goat) and One switches to A calculating that the probability of a car behind A is 2/3. Before One is allowed to open…
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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 to do an expected value analysis. In order to do…
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