Question

In a 1970’s game show, a contestant was given a choice of three doors of which one contained a prize. The other two doors contained gag gifts like a chicken or a donkey. After the contestant chose an initial door, the host of the show then revealed an empty door among the two un-chosen doors, and asks the contestant if he or she would like to switch to the other un-chosen door. The question is should the contestant switch. Does the probability of winning increase by switching to the remaining door?

Answer 1

This is often called the "Monty Hall" problem

Here is one explanation of the solution.
http://coastaltech.com/monty.htm