Game Show or Monty Hall Problem

Many consider probability to be just calculations based on common sense, but the Monty Hall problem is a clear example of how even a simple problem can have a counter-intuitive solution:

Game Show or Monty Hall Problem

  
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 In 1990 Marilyn Vos Savant had this problem sent in to her "Ask Marilyn" column for Parade magazine.  The problem is easy to state but the answer Marilyn provided was counter-intuitive and unleashed a storm of controversy...

Marilyn Vos Savant and the Game Show Problem

The Numberphile Channel 

provides a good video summary of the problem and its solution:

The  University of California Math Website provides a detailed explanation of the problem as well as information on its history:

The Monty Hall Problem