1.3 Cars and goats: the Monty Hall dilemma On Sunday September 9, 1990, the following question...
126. An article entitled "Behind Monty Hall's Doors: Puzzle, De- bate and Answer?" appeared in the Sunday New York Times on July 21, 1991. The article discussed the debate that was raging among mathematicians, readers of the "Ask Marilyn" column of Parade Magazine and the fans of the TV game show "Let's Make a Deal." The argument began in Septem- ber, 1990 when Ms. Vos Savant, who is listed in the Guinness Book of World Records Hall of Fame for...
Question 1: Consider the following Monty Hall problem. Suppose you are on a game show, and you are given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what is behind the doors, opens another door, say #3, which has a goat. Here we assume that the host cannot open the door to expose the car and when he can open either of...
5. Consider the Monty Hall Problem. A game show host shows you three doors, and indicates that one of them has a car behind it, while the other two have goats. You win a car if you end up choosing a door with a car behind it. The game is conducted as follows: • You pick an initial door out of the three available. • The game show hosts then opens a door (out of the remaining two doors) with...
Monty Hall Problem - Suppose you are going to be on a game show, and you will be given the choice of three doors: Behind one door is a car; behind the other two doors are 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...
The Game: Suppose you're on a game show, and you're given the choice of 3 doors. Behind one door is a car, behind the others, goats. You start by choosing a door, say number 1, which remains closed for now. The game show host, who knows what's behind the doors, opens another door, say number 3, which reveals a goat. He says to you, "You've already chosen door number 1, now that I've shown you a goat behind door number...
Now we modify it so that you are given the choice of four doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what is behind the doors, opens two other doors, say #3 and #4, each of which has a goat. Here we assume that the host cannot open the door to expose the car and when he can open two out of three doors, he chooses...
Consider the Monty Hall problem. Let’s label the door with the car behind it a and the other two doors b and c. 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 a and Monty chose b. (a) Make a 3 × 3 probability table showing probabilities for all possible outcomes. (3 marks) (b) Make a probability...
In the three-door Monty Hall problem, there are two stages to the decision, the initial pick followed by the decision to stick with it or switch to the only other remaining alternative after the host has shown an incorrect door. An extension of the basic problem to multiple stages goes as follow. Suppose there are four doors, one of which is a winner. The host says: You point to one of the doors, and then I will open one of...
Please help me write these in R script / Code 1, 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 #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He then says to you, "Do you want to pick door #2?" What is the probability of winning the car if...
agree or disagree Starting off, this was extremely confusing and difficult to understand everything. Playing the game, I originally thought of once one door was out of the way- I now have a 50/50 chance of winning the car. After the experiments of pick and switch, I found that my previous thought was incorrect! There are still three doors in this equation. Having one of the three revealed is an advantage now. I have found my percentage to be extremely...