The "Monty Hall" puzzle

Problem statement

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 can choose any door, and you'll receive what's behind it as a prize. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to stick with door #1, or switch to door #2?" Is it to your advantage to switch your choice of doors?

Solution to metapuzzle: show

Restated puzzle: show

Solution to puzzle: show

Comments: show

Source: Steve Selvin, in The American Statistician Volume 29, 1975 - Issue 1. Brought to public attention by Marilyn vos Savant in Parade, vol. 16, 1990-09-09

This is one of several pages on puzzles and metapuzzles.