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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 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, instead of three doors, we have four (or maybe $n$)…
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The Monty Hall problem

I was watching the movie $21$ yesterday, and in the first 15 minutes or so the main character is in a classroom, being asked a "trick" question (in the sense that the teacher believes that he'll get the wrong answer) which revolves around…
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Does Monty Hall logic apply to this real world situation?

I recently posted a tweet claiming I had encountered a real life Monty Hall dilemma. Based on the resulting discussion, I'm not sure I have. The Scenario I have 3 tacos (A,B,C) where tacos A and C are filled with beans, and taco B is filled with…
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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 morning. Suppose Monty has three apples. Two of them…
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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 answer to the problem is, and after coming back to…
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Question about Monty Hall if you already knew a bad door beforehand

So the setup of the scenario here is exactly the traditional Monty Hall problem. Except, before the game starts, you decide to cheat and open a door and it happens to be a goat. Before you can peek at the two other doors, the game begins, and you…
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Is this a modified Monty Hall problem (numbered doors)?

On a job interview, I got this question: Monty placed a car and two goats behind three identical doors (and the things do not move during the game). You receive the prize which is behind the door you picked in the second round. You choose door…
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Monty hall problem probability 2/6?

For the Monty hall problem, with 3 doors, two of which have sheep and 1 has a car. I calculated the probability of getting the car if you swap being 2/6 instead of 2/3. I have drawn this tree diagram of how I calculated it: And from it I get that…
yt.
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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 choosing both of the other two doors. If you decided to…
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If Monty Hall doesn't know where the prize is, should the contestant still switch doors, after Monty opens one door and unveiss a goat?

The other day I was asked a variation of the Monty Hall Problem. The answer of the original question is, of course, $ 66\% $ in favor of changing doors, but this is based on the fact that the game show host knows where the prize is. Suppose Monty…
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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 car behind one of them, then we have a 50/50…
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Subtle Twist on the Monty Hall Problem---Does It Make a Difference?

In the Monty Hall problem, when the host picks a door and reveals an goat, does it make any difference if he did not know which door the real car was behind, and he just happened to pick a door with a goat?
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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 three doors: behind one door is a car; behind the…
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Monty hall problem with 4 doors and PLAYER choosing 2 initially

Question: In a variation of the Monty Hall game show, you now have 4 doors and only one has a car behind it. The other 3 doors have goats. This time you choose (without opening them) 2 doors. Monty Hall opens one of the remaining doors and shows…
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Deal or No Deal: Monty Hall?

This question was inspired by another question posted today: Monty Hall Problem Extended. So I thought that the comments an answers brought up a great point about increasing the doors to 100 or something much larger, and using that as a way to help…
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