As stated, the answer is indeterminate. To demonstrate, consider these scenarios.
- Savant's Monty: The host knows where the car is, and wants to prolong the game. Switching wins 2/3 of the time.
- Ignorant Monty: The host has no idea where the car is. Revealing the goat was luck and your odds remain 50-50.
- Malicious Monty: The host knows where the car is, and wants you to lose. The fact that the host didn't reveal the car means that you have the right door. You'll have no chance of winning if you switch.
Nowhere in the problem are Monty's knowledge and motivation stated. When explained, most go along with the assumptions that Savant's argument introduces. When the actual Monty was asked, it turned out that he was usually ignorant. And the malicious scenario demonstrates how different the answer can be.
The fact that all three answers are consistent with the statement of the problem means that it is indeterminate.
- Savant's Monty: The host knows where the car is, and wants to prolong the game. Switching wins 2/3 of the time.
- Ignorant Monty: The host has no idea where the car is. Revealing the goat was luck and your odds remain 50-50.
- Malicious Monty: The host knows where the car is, and wants you to lose. The fact that the host didn't reveal the car means that you have the right door. You'll have no chance of winning if you switch.
Nowhere in the problem are Monty's knowledge and motivation stated. When explained, most go along with the assumptions that Savant's argument introduces. When the actual Monty was asked, it turned out that he was usually ignorant. And the malicious scenario demonstrates how different the answer can be.
The fact that all three answers are consistent with the statement of the problem means that it is indeterminate.