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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Reverse Monty Hall problem

First, we pick one door out of 100 doors. Then the host Monty Hall opens 98 doors out of the remaining 99 doors one by one. But this time he doesn't intentionally open the doors with goats. He just happens to. He didn't know which door had the car.…
Ryder Rude
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Monty Hall multi rounds variation

i was thinking about the Monty Hall problem lately and thought about a different game that is a variation of the original: There are $100$ doors. behind one of them there's a "$1$", behind all the rest there's a "$0$". you begin the game with $100$…
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Monty Hall Problem confusion

I have recently learned of the Monty Hall problem, where given three doors, you choose one with a 1/3 probability of choosing the correct door, and then switching to the other door changing the probability of choosing the correct door to 1/2. I am…
John Kent
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Is this proof of the Monty Hall problem correct?

The Monty Hall problem can be stated as follows: 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…
Adam
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Monty Hall variant with sequential decision making

There are $n$ doors, only one has a prize behind it. You can pick one at the beginning. At every round, host will open a door (which is empty) and ask you if you want to switch. The game will last $n-2$ rounds. I think the optimal strategy is to…
Ziqian Xie
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Question about Monty Hall problem

I'm having a bit of trouble understanding this particular version of the Monty Hall problem. Say that there are 5 doors, and I pay \$100 to switch doors, with a potential reward of \$1,000. If I switch doors, what is my expected winning value? In…
agra94
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Monty Hall Problem - Toss a coin to decide if I switch the door.

I know the basic Monty Hall problem and that I should decide to change the door after the first negative door is opened. But let's say my gut feeling says, stay with the door you took and I want to give the door a 50% chance to be picked. Therefore…
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What is the probability that the last coin of 10 coins flipped, (i.e. after 9 coins have been flipped), will be heads?

For a sequence of 10 coin flips, the probability of all heads is 1 in 1024 i.e. $$1/2^{10}.$$ And the probability for an individual coin flip to be heads is $1$ in $2$. After $9$ coins have been flipped, is the probability of the last coin being…
JDS
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What are the various explanations to arrive at the solution of Monty Hall Problem?

Possible Duplicate: The Monty Hall problem I want to know what are the various ideas which you might have come across to arrive at the solution of the Monty Hall Problem ? My idea is to get them all under a single page which would significantly…
Bhargav
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How to simulate Monty Hall problem in computer?

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 [but the door is not opened], and the host, who knows what's behind the doors, opens another…
Charles Bao
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A slight variant of the Monty Hall Problem.

Suppose that there are 4 doors having 2 cars and 2 goats. You arbitrarily choose a door, then Monty shows a door with a goat. What is the probability of getting a car if you switch. Apparently the answer is 3 / 4. I got it right but the line of…
Jansen Lopez
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Unknown Card Monty Hall

I'm trying to understand this problem better and whether or not it is defined as a variant of the classic Monty Hall problem. Let's say there are X cards in a deck of cards. A copy of this deck of cards is used by everyone, so only 1 player uses…
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Does a "guarantee" change probability? (variation of three card problem)

This is a variation of a probability question (Bertrand's box, or the three card / two color question) that's been asked many times before. However, this question relates specifically as to whether or not a guarantee can change the outcome. Here is…
user222002
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Monty hall - random goat reveal

This is a variation of the famous Monty Hall problem. I assume you know the usual setup. Here, the host behaves a bit different: The host knows what lies behind the doors, and (before the player's choice) chooses at random which goat to reveal. He…
jacob
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Probablilty - Monty Hall problem

A candidate chooses a door (which remains closed at first), so that he can win a car behind. Moderator opens n-2 other doors with goats. 2 doors remain closed. We consider the goat problem for n=5 and assign the following numbers to doors: The…
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