One day you decide to go out to buy a new puzzle book at the massive Honty Mall. When you enter, however, you are confronted by three doors and a rather dishevelled amateur philosopher who swiftly talks you into trying out a variation of an old game show puzzle (you obviously like puzzles, so it was an easy task).
The puzzle is put to you as briefly yet comprehensively as possible:
- There are three doors, there is a goat behind two of the doors and behind the third is a car.
- If, at the end of the game, you open the door with the car behind it, you win the car.
- First, you select two doors (not the one door of the Classic Monty Hall Problem).
- The philosopher will then open one of the doors you selected, revealing a goat.
- You then have the option to switch from your remaining selected door or stay.
- Before being allowed to open a door, you must provide the likelihood that a switch will win you the car (even if you choose to stay).
- The placement of the goats and car is randomised.
Do you switch or stay, and what is the likelihood of winning from a switch?
Note that we are assuming that you want a nice new car, rather than a goat!