### Problem

On the game show
"Let's make a deal", Monty Hall (the host) walks up to a contestant and
gives them $100 unless they want to play "the three doors". They
usually turn down the money and play "the three doors". Now behind one
of the doors is an enourmous cash prize, behind the other too are silly
prizes such as a years supply of toilet paper or a goat. So Monty asks
this same contestant to pick a door, which they do. Then, before
opening the chosen door and revealing what's behind it, he opens one of
the other doors which reveals one of the lesser prizes. Monty then
gives this contestant the option of staying with their chosen door or
switching to the other door which still remains closed. The contestant
then decides what to do and is rewarded with whatever prize is behind
the door they finally chose. So the question is, should the contestant
switch or stay?

### Solution

http://en.wikipedia.org/wiki/Monty_Hall_problem