The Monty Hall Problem: stick or switch?
The Monty Hall Problem is nice brain teaser, based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990 (Internet Archive [1] ) 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? The answer is YOU SHOULD ALWAYS SWITCH! Crazy eh? Not really if you think about it in basic simple probabilistic terms. Let's try. At the beginning of the Game, each door is equally probable to hide the car, so 1/3. We really cannot do much about it, we