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, Monty Hall, who knows what’s behind the doors, opens another door, say No. 3, and reveals 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 Monty Hall problem is described in more detail on wikipedia. It was made famous by the author Marilyn vos Savant in a magazine article. Apparently lots of people, including the famous mathematician Paul Erdős, remained unconvinced whether it was an advantage to switch doors or not. What finally convinced him was a computer simulation demonstrating the result predicted by vos Savant.
Your task is to write that simulation to convince a doubter like Erdős. Should you switch your choice of door, or retaining your original door choice? Simulate 1000 games with each strategy and show which one is most likely to see you drive home in a new car.