If you have ONE choice, the odds are 50/50. Previous choices are moot. They are gone, they do not exist. They do not impact subsequent choices. Soooo, you have ONE choice. And the odds are 50/50 that your choice will win or lose. Period.

This is not socks in a drawer. This is A OR B and it's defined as such. They are asked to make A choice between TWO doors. One OR... OR... OR... the other door... THAT is 50/50.