That is why the original 1/3 probability remains attached to your first door, while the 2/3 probability effectively transfers to the remaining unopened door.
A Simple Way to Understand It
Imagine the game had 100 doors instead of three.
You choose one door.
Your chance of picking the car is just:
1 out of 100.
That means there is a 99 out of 100 chance that the car is somewhere among the 99 other doors.
Now imagine the host knows where the car is and opens 98 doors, showing you goats behind every one.
Only two doors remain closed:
your original door and one other door.
Would you really believe your original door suddenly became a 50% chance?
Probably not.
Your original door still has its original 1% probability.
The other remaining door carries the other 99% probability.
The three-door version works according to the same principle.
The Answer
So, if you ever encounter the classic Monty Hall Problem and the host follows the usual rules, switching doors gives you the better strategy.
