So, we all know the Monty Hall problem. Where there are 3 doors with one winning door.
The contestant picks a door, then the host removes a non-winning door from the remaining two. Then the contestant is given the option of switching doors.
The originally selected door has a 33.33% chance of being the winning door, but the remaining door has a 66.67% chance of being the winner.
However, if this is done Deal or No Deal style, and the contestant gets to pick a second door in hopes that it's a non-winning door the probability changes.
Let's say the contestant successfully chooses a non-winning door, and is left with the same proposition as the Monty Hall problem. Where he has the option to swap the originally selected door with the one remaining door.
Now, the probability is 50% for each door.
Why? Why does it matter when the door is removed by the host (who knows which door is a winner), compared to by the contestant who removed the proper door by chance?