I have tried asking chatgpt, i have tried searching animations, I just dont get it!
Edit: I finally get it. If you choose a wrong door, then the other wrong door gets opened and if you switch you win, that can happen twice, so 2/3 of the time.
In: 296
There are 3 doors and 1 car. Car could be behind door A, B, or C. The ‘X’ represents the car:
| A | | B | |C |
| X | | | | |
| | | X | | |
| | | | | X|
Here you clearly see the 3 possibilities. Let’s say you choose “A.” In one out of the 3 possibilities, you selected the door where the car already is, and switching from A to B or C means you lose the car.
However, in 2/3 of the scenarios, you have chosen A where the car is actually behind B or C. If you get shown the empty door, then you will 100% choose the correct door by switching. Remember, this scenario happens 2/3 of the time, so by switching you actually have 2/3 probability.
This is, again, because in the scenario where you were already on the car, that only happens 1/3 of the time. By not switching, you keep your odds at that same 1/3 for the initial guess. By knowing an extra door and switching, your odds improve to 2/3.
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