Do you switch doors in the Monty Hall problem?

The Monty Hall problem is deciding whether you do. The correct answer is that you do want to switch. If you do not switch, you have the expected 1/3 chance of winning the car, since no matter whether you initially picked the correct door, Monty will show you a door with a goat.

Why is the chance not 50/50 in the Monty Hall problem?

After the contestant’s initial pick, Monty opens 999,998 doors with goats behind them and o↵ers the choice to switch. In this extreme case, it becomes clear that the probabilities are not 50-50 for the two unopened doors; very few people would stubbornly stick with their original choice.

What is the correct answer to the Monty Hall problem?

If the car is behind door 1, Monty will not choose it. He’ll open door 2 and show a goat 1/2 of the time. If the car is behind door 2, Monty will always open door 3, as he never reveals the car. If the car is behind door 3, Monty will open door 2 100% of the time.

Is the Monty Hall problem a conditional probability?

The Monty Hall problem is a famous, seemingly paradoxical problem in conditional probability and reasoning using Bayes’ theorem. Information affects your decision that at first glance seems as though it shouldn’t. In the problem, you are on a game show, being asked to choose between three doors.

How to understand probability using the Monty Hall problem?

Understanding Probability using the Monty Hall Problem. (see below for the 4 door problem) This problem is named after the Monty Hall game show. There are 3 doors, an Auto behind one, goats behind the other two. You pick a door. Monty, knowing where the car is, opens one of the others, revealing a goat.

Who is the host of Monty Hall problem?

The host, Monty Hall, picks one of the other doors, which he knows has a goat behind it, and opens it, showing you the goat. (You know, by the rules of the game, that Monty will always reveal a goat.) Monty then asks whether you would like to switch your choice of door to the other remaining door.

What happens if you pick the wrong door on Monty Hall?

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?”.

What is the probability of picking four doors?

Explain the Monty Hall problem in the case of 4 doors computing specific probabilities. I got that you have 1/4 chance of picking the door with the goat. 1/4 chance to pick the door with the prize and so on. 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. if you don’t switch