doors left, but that's actually not true!
the answer: you should always switch your choice!
the explanation: when you first picked one of the three doors, you had a 1 in 3 chance of picking the door with the prize behind it, which means you had a 2 in 3 chance of picking an empty door. what people get wrong here is thinking that because there are only two doors left in play, you have a 50 percent chance your first choice was correct. in actuality, your chances never changed.
there's still a 1 in 3 chance you picked the right door and a 2 in 3 chance you picked an empty door, 