The Monty Hall Problem

In class we discussed and debated the logic behind the ubiquitous “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? (Parade Magazine, Whitaker 1990)

Here is a simulation and an explanation of the answer.