The answer is yes.
The chances of finding the car double.
The solution can be illustrated as follows. There are three possible scenarios, each with 1/3 probability:
The player chooses the goat number 1. The driver chooses the other goat, the number 2. Changing, the player wins the car.
The player chooses the goat number 2. The driver chooses the other goat, the number 1. Changing, the player wins the car.
The player chooses the car. The driver chooses a goat, no matter what. Changing, the player finds the other goat.
In the first two scenarios, changing the player wins the car; in the third scenario the changing player does not win. Since the “change” strategy leads to victory in two out of three cases, the chances of winning by adopting the strategy are 2/3.
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