Given that a contestant on the Monty Hall Show has a choice between 3 doors. 1 door has a new car that the contestant wants. 2 doors each have a goat, which the contestant doesn’t want.
After the contestant chooses a door which has a 1 in 3 chance of being the new car, Monty Hall opens one of the other doors to reveal a goat. Monty Hall then offers to allow the contestant to change which door the contestant chooses.
Should the contestant change which door they chose to the other of the two remaining doors?
There is a 1 in 3 chance that the contestant chose the door with the car. There are 2 out of 3 chances that the contestant chose the door with a goat.
If the contestant choses the door with the new car, which happens 1 time out of 3 games, then Monty Hall will eliminate one of two goats. If the contestant always changes the door, then the contestant will lose 1 out of 3 times.
If the contestant choses a door with a goat, which happens 2 times out of 3 games, then Monty Hall will eliminate the other goat. If the contestant always changes the door, then the contestant will win 2 out of 3 times.