|
In her weekly Ask Marilyn column in Parade magazine, Marilyn vos Savant answers questions about physics, philosophy, and human nature. She also solves mathematical and logic problems (and that's where Monty Hall comes in). She started writing this column after being featured in a Parade article for her high IQ and then responding to a selection of questions in a follow-up article.
Perhaps you remember her response to what has been dubbed "the Monty Hall problem," named after the host of the classic game show Let's Make a Deal:
Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, and behind the other two doors are goats. You pick a door, say door #1, and the host, who knows what's behind the doors, opens another door, say door #3, which has a goat. He says to you: "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?
In a 1990 column, she responded that you'd have a better chance of winning if you switched doors. This led to all sorts of responses from academics and other readers — much of it criticism of her answer. She was, of course, found to be correct.
Why was Marilyn correct? Consider the situation in which the car is behind door #1 and goats are behind doors #2 and #3. The game show host is always going to show you one of the goats.
- If you pick door #1, the host will show one of the goats behind door #2 or door #3, and if you switch, you lose.
- If you pick door #2, the host will show you door #3; so if you switch to door #1, you win.
- If you pick door #3, the host will show you door #2; so if you switch to door #1, you win.
You win two-thirds of the time if you switch. This same chance will appear, no matter where you put the car and where you put the goats.
Marilyn, in addition to writing her column, is Chief Financial Officer of Jarvik Heart and assists her husband, Robert Jarvik, with cardiovascular disease research.
|
