Monty hall problem probability questions and answers. I understand the reasoning but it just feels wrong.

Is there a neater way in which to define this probability measure? Sep 13, 2017 · So you should always switch, a result which is not surprising as this problem is qualitatively the same as the original Monty Hall problem. Let R be the event “the prize is behind the door you chose initially,” and W the event “you win the prize by switching doors. He also covers perceptual biases including prosecutors fallacy, regression and Jul 29, 2017 · 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 picked the door with the car behind it. Assume that you always then switch to the last remaining door. After that, the participant is always offered the option of Statistics and Probability; Statistics and Probability questions and answers; Consider a version of the Monty Hall problem (Example 10. Let R be the event “the prize is behind the door you chose initially," and W the event “you win the prize by switching doors. You pick Door 1 and open Door 2. (Monty Hall problem) In the television game show Let's Make a Deal, the room is equipped with three doors. 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 visualize why switching is always the best choice when trying to explain the problem to others. Let’s label the door with the car behind it a and the other two doors b and c. But now, instead of always opening a door to reveal a goat, Monty instructs Mar 6, 2016 · In the Monty hall problem, the host chooses which doors to show you (or to show you which answers are incorrect). Behind one door is a reward (say, a car), while behind the other two doors are nothing (say, goats). Here’s a variation of Monty Hall’s game: the contestant still picks one of three doors, with a prize randomly placed behind one door and goats behind the other two. Then, the MC shows Door B, no car. However, the answer now is that if you see the host open the higher-numbered unselected door, then your probability of winning is 0% if you stick, and 100% if you switch. In fact, if the contestant switches doors after the host reveals a goat, their chance of winning the car is 23 2 3, not 50 50 50 50. 3. May 21, 2016 · It seemed like there was some confusion here, partially about the question and partially about the answer. One implication is that when the reduction of ignorance granted by the host is more transparently connected to the physical circumstances, the solution to the problem becomes Question: The problem is a take on the classic probability problem known as the “Monty Hall Problem”. In this version, there are 8 boxes, of which 1 box contains the prize and the other 7 boxes are empty. 5 "Monty Hall Problem" and Chapter 6 "Problems with Probability", Wheelan covers a range of practical applications including taste tests, lotteries, and extended warranties. A famous problem exists in probability, known as the Monty Hall problem. Feb 10, 2024 · For Monty to stick with his first choice and win ( S2W S 2 W ), he must choose the right door ( A A) first. To fully grasp the Monty Hall problem, it's essential to understand that the initial choice matters, and the host's action of revealing a goat door Statistics and Probability questions and answers; 1) The Monty Hall problem is a counter-intuitive statistics puzzle: - There are 3 doors, behind which are two goats and a car. Compute P(W|R) and P( WRC). 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 number of doors, the probability of winning the car by switching approaches 1. Assume that there are four doors A, B, C and D. 4 Define the structural model that corresponds to the Monty Hall problem, and use it to describe the joint distribution of all variables. The contestant does not know where the car is, but Monty Hall does. 1 out of 4 times door 1 and door 2 will be wrong and the car is behind door 3. This question is based on a variation of the Monty Hall problem. May 22, 2014 · Extended math version: http://youtu. Compute P(W |R) and P(W | R°). In both cases, after Monty opens some doors, you have more information about the location of the prizes than you did before the doors were opened, so you have a better chance of making the right decision. A new car is behind one of the three doors, but you don't know which. 5 (Monty Hall) Prove, using Bayes’ theorem, that switching doors improves your chances of winning the car in the Monty Hall problem. Or if door 1 doesn't have a car behind it then Monty picks either door 2 or 3 with certainty. Start by understanding that this is a case of conditional probability, where the host's action of opening a door without the car affects the probability of finding the car behind the remaining doors. Assume that a room is equipped with three doors. Statistics and Probability; Statistics and Probability questions and answers; 3. If you are on the show, here’s what happens: Monty shows you three closed doors and tells you that there is a prize behind each door: one prize is a car, the other two are less valuable prizes like peanut butter and fake finger nails. Suppose that the game show has N doors in total. Suppose that you are on a television game show. But that scenario is extremely unlikely , the chance of that is one in 500,000. The Monty Hall Problem, according to Chance magazine, has been used to study decision making in business schools at Harvard and Stanford. This problem, known as the Monty Hall problem, is famous for being so bizarre and counter-intuitive. The Monty Hall Problem is a famous problem in probability that originated from a game show on television. " a. Let's say you pick door 1. Dilip Sarwate's answer describes the "standard rules" of the two-player game in which this cannot happen: Monty will always throw one player out of the game rather than open the unchosen door. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975. Question: (a) In the Monty Hall problem with 100 doors, you pick one and Monty opens 98 other doors with goats. You pick a door, say No. Behind one of these doors is a car; behind the other two are goats. , door A), conditional on the host having opened door B, then what is your probability of winning? 2. Initially, choosing a door has a probability 1/ 3. Study question 1. Apr 1, 2023 · $\begingroup$ @Ghost Self-answer questions are allowed. If the coin lands Heads, Monty resolves to open a goat door (with equal probabilities if there is a choice). You randomly pick one of them, and the host will open one of the other two doors, behind which is a goat. It’s a choice of a random guess and the “Champ door” that’s the best on the other side. Statistics and Probability. Let’s say Monty asks you to choose between N doors where N is more than or equal to three. You pick a door and the game organizer, who knows what’s behind the doors, opens another door which has a goat. Behind one, chosen at random, is a new Ferrari and behind the other two are goats. Take the case where there are 6 doors. Originally proposed by Steven Selvin in a Letter to the Editor of the American Statistician in 1975, the problem examines a common choice on the game show "Let's Make a Deal" (which was hosted by Monte Question: The Monty Hall problem is a classic probability puzzle that involves a game show where a contestant is given a choice between three doors. Jun 20, 2019 · The Monty Hall problem is based on one of the regular games on the show. That's it. In the case that door 1 has the prize behind it, suppose that Monty opens one of the other two doors for you not uniformly at random, but rather opens door 2 with probability p and door 3 with probability 1 − p, for some p ∈ [0, 1]. For example, how the question is posed to the warden can affect the answer. Behind two are goats, and behind the third is a shiny new car. You initially pick door The game show host, Monty Hall, who knows where the Ferrari is, then opens one Statistics and Probability; Statistics and Probability questions and answers; Could you answer the questions from the monty hall problem using conditional and total probability ? 1. Statistics and Probability questions and answers; This tutorial covers the Monty Hall problem and its extensions, the birthday problem, and joint probability. If one wishes to compute the probability that the host opens door 3 then one can find it by conditioning on the location of the prize: = 1/2 × 1/3 + 1 × 1/3 + 0 × 1/3 = 1/2. Behind the other three are goats. I understand the reasoning but it just feels wrong. The contestant picks a doo …View the full answer Statistics and Probability; Statistics and Probability questions and answers; 3. - Monty Hall, the game show host, examines the other doors (2 & 3) and opens one with a goat. Statistics and Probability questions and answers. He also covers perceptual biases including prosecutors fallacy See Answer. Apr 20, 2019 · The combined probability of #1 and #3 will thus be 1/3 and the combined probability of #2 and #4 will be 2/3. 13) where there are four doors rather than three. ” a. 1: The car and the two goats. be/ugbWqWCcxrg?t=2m32sA version for Dummies: https://youtu. b. After the contestant selects a door, the host, who knows what is behind each door, opens one of the remaining doors to reveal a goat. Part 1 Multiple Choice Questions This video demonstrates the Monty Hall Problem, named after the host of the game show "Let's Make a Deal" that originally aired in the 1960s and 1970s. Now initially suppose We select door 1. Our professor asked us to add a few extra details to the problem as follows: (c) Determine the winning probability of the following strategy: after the host opens door B, the player flips a fair coin, and he will stick to door A if he gets the head, otherwise he will switch to door C. Summary of Problem: Inder Gill tried two different Bayesian formulations of the Monte Hall problem and got two different answers Statistics and Probability questions and answers; Consider a modified version of the Monty Hall problem. The Monty Hall Problem: The Monty Hall problem is an exereise in probability who's results are counterintuitive to most people. Math; Statistics and Probability; Statistics and Probability questions and answers; 2. (d) Here's been a bunch of questions on the Monty Hall problem, so I'll assume people know the basics. The P(that you chose the door with the car behind it) = 1/N. So you should switch. Behind one door is a prize, while the other two doors hide goats. We can look at this problem in a different way. The Monty Hall problem is based upon a US game show called “Let’s Make a Deal”. In my opinion, the reason it seems so bizarre the first time one (including me) encounters it is that humans are simply bad at thinking about probability. ) is “98 percent accurate”, it would be wise to ask them what they mean, as the following example will demonstrate: Explain the Monty Hall problem in the case of 4 doors computing specific probabilities. The Monty Hall Problem gets its name from the TV game show, Let's Make A Deal, hosted by Monty Hall 1. and if Monty opens a door and gave choice to swich the probability of staying with first …. A car is behind one of the doors, while goats are behind the other two: Figure 13. Ron Clarke takes you through the puzzle and explains the counter-intuitive answer Statistics and Probability questions and answers. Unfortunately, there are only goats behind the other two doors. 8. a Question 3 Consider the following modified version of the Monty Hall problem. Select one to make your choice! Cards, dice, roulette and game shows Use the binomial probability formula to find P (x). Welcome to the most spectacular game show on the planet! You now have a once-in-a-lifetime chance of winning a fantastic sports car which is hidden behind one of these three doors. The other two doors hide “goats” (or some other such “non-prize”), or nothing at all. Monty Hall Problem 1) If you stick with your original choice (i. Behind one door is a car and behind the other two are goats. The Monty Hall problem may well be the best-known counterintuitive problem in probability, but it is certainly not the only one. 14 Recall the Monty Hall problem from Section 1. The "paradox" assumes that probabilities of #1 and #2 are zero, implying that #4 is twice as great as #3, but that version of the game doesn't coincide with the actual game show hosted by Monty Hall. The Monty Hall Problem is a famous probability puzzle where a contestant chooses one of three doors, with a car behind one and goats behind the others. If you stick with your original choice (i. Before the door is opened, however The Monty Hall problem is a counter-intuitive statistics puzzle: There are 3 doors, behind which are two goats and a car. Monty helps us by “filtering” the bad choices on the other side. 0. Thus our chance of getting a car if we always switch is 99 100 ∗ 198 = 99 98 100 99 100 ∗ 1 98 Here’s the key points to understanding the Monty Hall puzzle: Two choices are 50-50 when you know nothing about them. View the full answer. The answer actually depends on some crucial assumptions. 10. 2?" Statistics and Probability; Statistics and Probability questions and answers; The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. Behind one door is the prize, and behind the other (N−1) doors, goats. if I pick an empty door you have a 1/2 chance of doing this in this case you have 1/2 chance of winning the prize. See Answer. Dec 1, 2015, 5:00 AM PST. Otherwise, Monty resolves to open a random unopened door, with equal probabilities. Analyze the “Monty Hall Problem” which is stated as follows: There are three doors, numbered 1, 2, and 3. 6. Share. Hall's imagination. The contestant aims to walk away with the highest possible value, hence does not necessarily mean he has to walk away with the car prize (IE highest possible prize value) probability. Behind two are goats, and behind the third is a car. Jun 23, 2015 · Our probability of picking a goat initially is clearly 99 100 99 100. Why the paradox? The tendency of people to provide the answer 1/2 is likely due to a tendency to ignore context that may seem unimpactful. Without him you have this. Question: The problem is a take on the classic probability problem known as the “Monty Hall Problem”. After you choose a door, the host opens one of the doors you didn't choose to reveal a Jan 21, 2007 · The Monty Hall Problem is a famous (or rather infamous) probability puzzle. I noticed that all the info was sorta disparate and floating around, so I decided to organize everything here. Behind one of them is a car. 18 (The Monty Hall problem) Suppose there are three doors, labeled A, B, and C. But since Door 2 is a loser, Door 3 must have a 2/3 probability of being a winner. Intuitively, this makes Question: The problem is a take on the classic probability problem known as the “Monty Hall Problem”. As an example, Marily vos Savant's statement of the problem as it is quoted in the Wikipedia article is imprecise. 1 out of 4 times the car will be in door 1 and Door 2 is a goat. The easiest way to see this is consider two strategies: S) always switch the door and N) never switch the door. Once Monty opens one door with the goat, the probability that the car is in one of the other 2 remaining doors is 1/2 * 3/4 = 3/8 > 1/4. Estelle Caswell. One door has a car behind it, and the other three have goats behind them. be/7u6kFlWZOWgMore links & stuff in full description below ↓↓↓ Jan 24, 2019 · In the very unlikely case where Monty randomly (without knowing) opens 999,998 doors and doesn't find the car the two remaining doors will have a 50-50 probability. You select one box at first. Now matter which door he opens following it, he will win. Oct 15, 2023 · EDIT 1: Monty does not know the value of each door, only the door that contains the car. This question was inspired by another question posted today: Monty Hall Problem Extended. So, P(S2W) = 1 3 P ( S 2 W) = 1 3. , door C), conditional on the host having opened door Here’s the best way to solve it. conditional probability and Bayes’s theorem can be used to solve them: the testing problem, and the Monty Hall problem. In the Monty Hall dilemma, new information is provided by the all‑seeing host. In this show, contestants picked one of three curtains, one of which had a car behind it and the other two had goats. 1. What is the probability for the player to win by always switching to the only remaining door? 2. Math. Statistics and Probability; Statistics and Probability questions and answers; Consider a generalization of Monty Hall problem. Behind one of the doors, there’s a car and behind the remaining doors are goats. It is in fact best to switch doors, and this is not hard to prove either. Apr 23, 2022 · The Monty Hall problem involves a classical game show situation and is named after Monty Hall, the long-time host of the TV game show Let's Make a Deal. You are asked to pick a door, and will win whatever is behind it. Aug 8, 2017 · The key to the solution of the Monty Hall problem is that Monty Hall reveals one of the incorrect solutions after stage one. Oct 25, 2015 · 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. Monty Hall opens one of the remaining two doors, revealing a goat. Monty Hall, the game show host, examines the other doors …. The problem ends up being exclusively about the door that you choose versus the one that is left. You will pick a door and then the host will open 4 remaining doors revealing goats. What is the probability of winning (assuming you would rather have a car than a goat) if you switch to the remaining door? Explain your answer. The Monty Hall Problem – In a famous game show the participant is always giventhe choice of three doors. Then the probability of Door 1 being a winner is 1/3 and the probability of Doors 2 or 3 being a winner is 2/3. In Naked Statistics Chapter 5 "Basic Probability", 5. There are three doors labeled 1, 2, and 3. Yes, we are supposed to do conditional probabilities but the doors are not equally likely because the door that was opened did not have the prize and also the door that was open was not the initially chosen. They pick a door and the host, who knows what’s behind the doors, must always open another door to reveal a goat. 1, and the host, who knows what's behind the doors, opens another door, say No. This Monty Crawl problem seems very similar to the original Monty Hall problem; the only di erence is the host’s actions when he has a choice of which door to open. , door A), conditional on the host having opened door B, then what is your probability of winning? 2) If you switch to the remaining door (i. And it's called the Monty Hall problem because Monty Hall was the game show host in Let's Make a Deal, where they would set up a situation very similar to the Monte Hall problem that we're about to say. Please read about it online and share your thoughts on the problem. Jul 21, 1991 · After the 20 trials at the dining room table, the problem also captured Mr. Then, once we pick a goat and one goat door is opened, there are 98 other doors, of which one has a car. 11) Consider the Monty Hall problem, except that Monty enjoys opening door 2 more than he enjoys opening door 3, and if he has a choice between opening these two doors, he opens door 2 with probability p, where 1 2051 To recap: there are three doors, behind one of which there is a car (which you Jan 18, 2024 · Explaining the Monty Hall problem: Bayes theorem. This is not a traditional game, since it has no win or lose; it is an opportunity to explore an interesting probability question. N = 3 doors (i). The problem was made popular when Marilyn vos Savant published it in her Parade Magazine column. If Door 2 is shown to be a loser by the host's choice then the probabilty that 2 or 3 is a winner is still 2/3. In this show, contestants picked one of three curtains, one of which had a car behind it and the other two had Statistics and Probability questions and answers. Compute P(W) using the law of total probability. (040, Sec 2. Oct 22, 2015 · The OP is asking about the probability of winning given that Monty has opened the door that neither player chose. The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. He picked up a copy of Ms. Consider the Monty Hall problem. Monty, who knows where the prize is, then opens 6 of the remaining 7 boxes, all of which are shown to be empty. You’re hoping for the car of course. It is structured so that you will read some information, and maybe watch a video, on a given topic, and then you will be asked a few questions to ensure that you understood what you learned. I teach middle and Oct 18, 2023 · The Monty Hall problem is famous because it defies our intuition. (b) Suppose Monte opens 98 doors without checking for cars. Jun 15, 2014 · The big problem with the "Monty Hall" problem is that there are many problems that sound superficially the same, but have different solutions. P (Keep and loose) = ⅔. Mar 28, 2019 · To do the Monty Hall problem you need Monty Hall. Let R be the event "the prize is behind the door you chose initially," and W the event "you win the prize by switching doors. You do not, unlike the host, have knowledge of what the incorrect/ correct answers are which I think is the fundamental difference between the situations. Dec 17, 2013 · By picking one of the doors first, the probability of getting a car is 1/4. Can you link the problem to some of the concepts we learned in this chapter, such as conditional probability? Question: (The Monty Hall problem) Suppose you are on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. This means that the probabilities are as follows: We will assume Door 1 is the car and Door 2 and 3 are sheep. A player chooses Door A. if you don't switch. Statistics and Probability questions and answers; Consider a modified version of the Monty Hall problem. You select one of the doors, say, door A. The same answer to the Monty Hall problem can be obtained using the Bayes theorem. With this, we conclude the Monty Hall Problem Explanation using Conditional Probability. The host then opens one of doors B or C, as follows: If the car is behind B, then they open C Oct 4, 2021 · For me, it’s 1 (I peeked). consider the Monty Hall problem for n-door. Instructions. He then says to you, "Do you want to pick door No. The terms of the game have to be stated very precisely. . vos Savant's original column, read it carefully, saw a loophole and then Statistics and Probability questions and answers. In the monty hall problem, the probability concept is used is as follows: There are 3 doors, behind two of which is a goat and behind one of them is a winning prize. Suppose that after the host opens all remaining doors except B, the player flips a fair coin, gets the tail, and this entails him to switch to door B. So in that case you could say you have a chance of 1 500000 1 500000 to get a 50-50 chance. So, the probability of him winning is 1/3 1 / 3, whether he makes the switch or not. Question: 10. Let's now tackle a classic thought experiment in probability, called the Monte Hall problem. Aug 19, 2020 · P (Keep and win) = 1/3. In Monty Hall problem, if we change the door chosen after the host has opened one of the gate witho …. The contestant knows p but does not know the outcome of the coin flip. 7. Suppose you initially pick Door 1. 1 Hypothesis Testing If someone tells you that a test for cancer (or alchohol, or drugs, or lies etc. Question: This question is in regard to the Monty Hall problem in statistics. Question: Consider the following variant of the Monty Hall problem. The Monty Hall Problem is an example of a simple probability problem with an answer that is counterintuitive. This is a case of conditional probability. 3, which has a goat. Compute P( WR) and P( WRC). In the game the contestant chooses a door and then Monty chooses a door, so we can label each outcome as ‘contestant followed by Monty’, for example ab means the contestant chose Part I - Multiple Choice Questions This video demonstrates the Monty Hall Problem, named after the host of the game show "Let's Make a Deal" that originally aired in the 1960s and 1970s. That leaves cases 4 and 5 each with a ⁠ 1 / 3 ⁠ probability of occurring and leaves us with the same probability as before. Economics questions and answers. by Estelle Caswell. Then, after stating the question in the posting, the poster should provide the answer in a separate answer box. Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Suppose that you choose door 1. Dec 5, 2020 · Study question 1. Dec 1, 2015 · The math problem that stumped thousands of mansplainers. So our chance of switching from a goat door to a car door is 198 1 98. Problem 8 (Conditional Probability) (10 points). The probability that you chose the door with the car behind it = 1/N. Jul 13, 2024 · The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The Monty Hall Problem. monty-hall. - You pick a door (call it door 1). 1 out of 4 times the car will be in door 2 and you see the car. n=5, x=3, p=0. There are many versions of solutions to this problem, but many of them are not complete. 5. 1/4 chance to pick the door with the prize and so on. Imagine you are at a game show, where you are given three doors. In your exam, the person who can "show you" incorrect answers is you. The Monty Hall problem is a great introduction to this powerful tool as it uses a quantity related to our degree of belief in the occurrence of the event, an approach rooted in the Bayesian interpretation of probability. e. The scenario is such: you are given the opportunity to select one closed door of three, behind one of which there is a prize. The problem is stated as follows. You pick a door (call it door A). Apr 8, 2019 · So, what is the Monty Hall Problem? We can start with this amicable question from 1996, which began with a clear statement of the problem and its correct answer: Probability: Let's Make a Deal I have been having difficulty understanding certain aspects of the "Let's Make a Deal" problem, and I was hoping you could help me. Statistics and Probability; Statistics and Probability questions and answers; The Monty Hall Problem – In a famous game show the participant is always giventhe choice of three doors. The contestant can then stick with their original choice or switch to the other unopened door. On September 9, 1990, a reader of Marilyn vos Savant's Parade Magazine The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall. Advanced Math questions and answers; Consider the Monty Hall problem discussed in lecture. Question: (5 pts; Monty Hall Problem, probability space). Now …. In that event, the poster is expected to start with the posting with something like "This is a self-answer question". Nov 16, 2020 · Of course, the probability a car is behind a given door is 1/3, and if door 1 does have the car behind it then Monty can pick either door 2 or 3 with probability 1/2 each. The game show host (Monty Hall) invites you to pick a door. Before each show, Monty secretly flips a coin with probability p of Heads. The many counterintuitive results that can be found in probability have attracted much attention from cognitive psychologists, particularly those who endorse the heuristics and biases approach. Let’s say Monty asks you to choose between N doors where N >=to 3. May 15, 2017 · 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. The rules are as follows: Jul 4, 2020 · Here is a possible formulation of the famous Monty Hall problem: Suppose you’re given the choice of three doors: behind one door is a car, each door having the same probability of hiding it; behind the others, goats. Behind 5 doors there are goats and behind 1 door there is a car. Same event, different knowledge, different probability. If you are not familiar with the Monty Hall Three Door puzzle, the premise is this: There is a prize behind one of three doors. I got that you have 1/4 chance of picking the door with the goat. wk cj ql xg wh me ev in mm mu