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).

192 questions
-1
votes
3 answers

Does Monty Hall Problem have any effect on an equation with multiple choices?

I am having a discussion with someone that insists the Monty Hall Problem would improve the probability of guessing the correct door. However, the circumstances are different. You have four doors. Only one has the right answer. We are not concerned…
-1
votes
2 answers

Monty Hall Problem - Strategy that maximizes chances of winning the prize

On a game show, there are three doors, behind one of which is a prize. I choose a door and the host opens one of the other doors that has no prize behind it. I get to switch my door choice if I wish. Now suppose we have three positive numbers…
Teta K
  • 1
  • 1
-1
votes
1 answer

How does the knowledge of one's preference for A over B affect the probability of one's preference for C over B if one's preference is transitive?

Suppose you know someone has preferences between the three pizza toppings pepperoni, olives and mushrooms. If you are told that they prefer pepperoni over olives then what is the probability that they also prefer mushrooms over olives if their…
user637421
-1
votes
2 answers

Is this informal solution to the Monthy Hall problem wrong? And why?

I recently opened my high school book about probability and statistics and I found an informal solution to the Monthy Hall problem. I translate it here: "Let's suppose that the first door chosen by the player is wrong and hides a goat. The host…
Camingo
  • 361
  • 2
  • 9
-1
votes
2 answers

Alternative analysis of the Monty Hall problem

The widely accepted answer for the Monty Hall problem is that it is better for a contestant to switch doors because there is a $\frac23$ probability he picked the door with a goat behind it the first time and only a $\frac13$ probability the he…
CrankyShaft
  • 119
  • 1
-1
votes
1 answer

The Wrong Answer of Monty Hall Problem

I know the correct answer is 2/3 for switching. And, I understand the reasoning behind that answer. But I still don't know why there exists another answer if I choose to do it another way Let's say I pick the first door and Monty open second hall…
Raymond Pang
  • 111
  • 2
-2
votes
1 answer

Monty Hall Problem + dice - Why does the probability of whining the car raises after switching doors?

I'm trying to understand the Monty Hall problem. When the contestant switches the door the probability of them winning a car is higher than if they continued with their first choice. Why would the probability change from 1/3 go up to 2/3 if both…
IgorAlves
  • 95
  • 4
-2
votes
3 answers

Monty Hall's problem argument

Let us take 3 doors A, B, C. Now, let us say car is in A. Now if player selects A, host opens B, on switching player loses. If player selects A, host opens C, on switching player loses. If player selects B, host opens C, on switching player wins. If…
aditya gupta
  • 310
  • 3
  • 16
-2
votes
1 answer

How often will two random integers between one and three (boundary inclusive) be the same?

Assuming the answer is one out of three? And, also, would this be a good distillation of how to understand the "Monty Hall" problem?
user92272
  • 1
  • 1
-2
votes
2 answers

Probability and the Monty Hall problem

In this video is explained that during the Monty Hall problem you have a $\frac {2}{3}$ probability of winning if you always switch and a $\frac {1}{3}$ probability of winning if you never switch. I understand the reasoning but it just feels wrong.…
Tim
  • 211
  • 1
  • 6
-2
votes
3 answers

Translation between Monty Hall and Gold bars problem

When I read this question (problem restated below), and the first comment, I was drawn to the great similarities between this problem and the Monty Hall problem (asking for the winning probability if you switch). Both include a choice with partial…
Arthur
  • 187,016
  • 14
  • 158
  • 288
-3
votes
1 answer

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
  • 1
  • 2
1 2 3
12
13