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?

Simple solution

The solution presented by vos Savant  in Parade shows the three possible arrangements of one car and two goats behind three doors and the result of staying or switching after initially picking door 1 in each case:

Behind door 1	Behind door 2	Behind door 3	Result if staying at door #1	Result if switching to the door offered
Car	Goat	Goat	Wins car	Wins goat
Goat	Car	Goat	Wins goat	Wins car
Goat	Goat	Car	Wins goat	Wins car

If you switch, you get the car with probability 2/3. So switching is always a good choice.