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How does the game show problem work?
An intuitive explanation is that, if the contestant initially picks a goat (2 of 3 doors), the contestant will win the car by switching because the other goat can no longer be picked, whereas if the contestant initially picks the car (1 of 3 doors), the contestant will not win the car by switching.
How do you play Monty Hall problem?
Monty Hall asks you to choose one of three doors. One of the doors hides a prize and the other two doors have no prize. You state out loud which door you pick, but you don’t open it right away. Monty opens one of the other two doors, and there is no prize behind it.
What’s the solution to the Monty Hall problem?
Below is the solution for the Monty Hall Problem: Suppose that the guest starts from door number 1 at first as selection and the host always shows any door other than the door number 1, which does not contain the car.
What happens if you pick the first door in Monty Hall?
The first row shows the scenario where you pick door 1 initially and the prize is behind door 1. Because neither closed door has the prize, Monty is free to open either and the result is the same. For this scenario, if you switch you lose; or, if you stick with your original choice, you win.
What is the probability of winning Monty Hall?
The only random portion of the process is your first choice. When you pick one of the three doors, you truly have a 0.33 probability of picking the correct door. The “Don’t Switch” column in the table verifies this by showing you’ll win 33% of the time if you stick with your initial random choice.
How is a goat revealed in Monty Hall?
As the guest picks one among the three doors, and then the host opens one door among the remaining two doors, is revealed to be a goat, the guest then has more information than the initial 1 in 3 choice which was random.