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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).

225 questions
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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…
jing3142
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Is this a Monty Hall Problem?

I asked the following question on an exam and want to verify I have the correct answer before marking it. “Your friend has three laptops that he wants to get rid of. He offers one of them to you. He then remembers that two of them have batteries…
Aleks
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Monty hall with $n$ doors and Monty opening $m$ doors

In Monty Hall problem generalized to $n$ doors, the Monty hall's problem was generalized to $n$ doors with Monty opening $m$ of them, where $m < n - 1$. The probability of winning by switching is $\frac{n - 1}{n(n - m - 1)}$. I am confused about…
user5965026
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Why's the probability of the unchosen doors' containing the prize reduced to the unopened door?

I understand, and ask not about, how to prove that you ought switch. Let $\Pr(✘)$ = probability that the unchosen doors have the prize (I chose the X mark to signify that you chose wrongly). Please see the question in the title. Monty knows which…
user53259
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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: Monty Hall opens one door with no car behind,…
Masutatsu
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In case player chooses winning door in Monty Hall, Do we need to consider reveling goat 1 and goat 2 as same choice or different choice in solution?

While solving Monty Hall Problem, In possible positions/choice table, There is a case where player initially chooses car (winning) position and host has to reveal either goat 1 position or goat 2 position. Here, do we need to consider both these…
Murali
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Monty hall is allowed to show a car

I am trying to solve the Monty Hall Problem with $3$ doors ($2$ goats, $1$ prize) with a simulation of the rules You initially pick a door randomly from the 3 possible doors. Monty hall does not know anything about the prize door and the goats…
Upstart
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Monty Hall problem five doors

Suppose you’re on a game show, and you’re given the choice of five doors: Behind one door is a car; behind the others, goats. You pick a door, and then the host, opens two of the doors, which guaranteed have goats. He then says to you, “Do you want…
Ritu
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