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In: Statistics and Probability

Monty hall Problem Explain the statistical probabilities associated with the game show

Monty hall Problem

Explain the statistical probabilities associated with the game show

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The Monty Hall problem is a famous problem loosely based on the game show Let's Make...
The Monty Hall problem is a famous problem loosely based on the game show Let's Make a Deal. You are a contestant on the game show. There are 3 doors in front of you. Behind one door is a prize, and behind the other two doors are goats. Assume the door with the prize is picked uniformly at random from the three doors. First, you pick a door. Then, Monty Hall will open one of the other two doors that...
(Monty Hall problem) Suppose you’re on a game show, and you’re given the choice of three...
(Monty Hall problem) Suppose you’re on a game show, and you’re given the choice of three doors, say Door 1, Door 2, and Door 3. Behind one door there is a car; behind the others, goats. Assume it is equally likely that the car is behind any door, i.e., P(D1) = P(D2) = P(D3). You will win whatever is behind the door you choose. (a) If you pick Door 1, what is your probability of winning the car? [2 point]...
2. (Monty Hall) Suppose you are on a game show and are presented with three closed...
2. (Monty Hall) Suppose you are on a game show and are presented with three closed doors marked door 1, 2, and 3. Behind one door is a prize and behind the other two are goats. Suppose the host allows you to select one door, but the following two rules apply: • Before it is opened the host opens one of the two unselected doors that has a goat behind it. • The host then allows you to switch your...
A variance of Monty Hall Problem. Let's say I am playing a game where there are...
A variance of Monty Hall Problem. Let's say I am playing a game where there are 6 doors, there is a car behind 2 doors and there are goats behind 4 doors. I don't know what is behind the doors but I want a car. Let's say I pick a door at random, so Initially, my chances of winning a car are 1/3. But before I open my door to see if I won, the host of the game opens...
Suppose Monty Hall wants to make his game show more interesting. In the new version, there...
Suppose Monty Hall wants to make his game show more interesting. In the new version, there are 7 doors and 2 cars behind the doors. The other 5 doors have goats behind them. A contestant picks a door. Monty Hall opens 3 of the doors with goats behind them (never the door that the contestant picked or a door with a car). The contestant then has the choice of switching doors.find the probability that the contestant wins a car if...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall)...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall) gives a contest a chance to choose from three doors of which one is a new car and the other two are goats. After the contestant chooses a door, the game show host who knows what is behind all of the doors decides to open another door behind which a goat sits. The games show host. then, offers the contestant an opportunity to switch...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall)...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall) gives a contest a chance to choose from three doors of which one is a new car and the other two are goats. After the contestant chooses a door, the game show host who knows what is behind all of the doors decides to open another door behind which a goat sits. The games show host. then, offers the contestant an opportunity to switch...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall)...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall) gives a contest a chance to choose from three doors of which one is a new car and the other two are goats. After the contestant chooses a door, the game show host who knows what is behind all of the doors decides to open another door behind which a goat sits. The games show host. then, offers the contestant an opportunity to switch...
(a) In the Monty Hall problem with 100 doors, you pick one and Monty opens 98...
(a) In the Monty Hall problem with 100 doors, you pick one and Monty opens 98 other doors with 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. (b) Suppose Monte opens 98 doors without checking for cars. What is the probability that, once the doors are open, changing your choice will not change your chances of winning.
1. (a) Consider a modified version of the Monty Hall problem. In this version, there are...
1. (a) Consider a modified version of 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. You select one box at first. Monty, who knows where the prize is, then opens 6 of the remaining 7 boxes, all of which are shown to be empty. If Monty has a choice of which boxes to open (i.e. if the prize is in the box you...
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