Question

Assume that you are on a game show, and are called on stage to play a game. The game involves three closed doors, behind two doors there is nothing and behind the third door is a prize. The host asks you to pick one door, and you will win behind it.

However, once you have chosen the door, the host does something strange. The host opens one of the remaining two doors and shows you there is nothing behind the door. (Unknown to you the host always shows you a door with nothing behind it).

The host now gives you a choice: would you like to stick with your initial door choice, or would you like to change to the remaining door (i.e. the door which neither you picked, nor the host opened)

What should you do? (Stay with the original door or Change Doors). Calculate your odds of winning in either circumstance and be explicit. Then decide what to do.

Answer 1