You find yourself on a game show and there are 10 doors. Behind nine of them are assorted, random farm animals including a variety of pigs, goats, and geese, but behind one is a brand-new, shiny, gold car made of real gold!
The game proceeds as follows:
This process continues until there are only two doors left, one being your current choice. (Every time the host opens a door, you are given another option to switch or stick with the one you currently have selected.)
If you play optimally, your chances of winning the car are of the form , where and are coprime positive integers.
Details and Assumptions:
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