Marilyn vos Savant, who was briefly listed in the Guinness Book of World Records as having the highest I.Q. on record, has a column in Parade magazine in which she answers readers’ questions.
In September 1990, Marilyn vos Savant devoted one of her columns to a reader’s question, which presented a variation of the 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 #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 pick door #2?” Is it to your advantage to switch your choice of doors?”
“Yes; you should switch,” she replied. “The first door has a 1/3 chance of winning, but the second door has a 2/3 chance.”
via pricenomics.
She received thousands of answers, almost all much like this one.
That’s how I would have answered, too, which goes to show my lack of ability to reason logically. It took me a long time to understand why Marilyn vos Savant was right, even after I read the explanations.
∞∞∞
Here is the clearest version of the explanation that I can give.
There are three equal possibilities for what lies behind Door #1—Goat A, Goat B or a car.
If it is Goat A, then there is a car behind Door #2.
If it is Goat B, then there is a car behind Door #2.
If it is a car, then either Goat A or Boat B is behind Door #2.
Therefore your chances of a car are two out of three if you switch to Door #2, and only one out of three (as before) if you stick with Door #1.
∞∞∞
I wonder whether readers of Parade magazine would have been so quick to reject the columnist’s answer if the column had been “Ask Marlon: the world’s smartest man asks the world’s most frequently asked questions.”
LINK
The Time Everyone “Corrected” the World’s Smartest Woman by pricenomics. (Hat tip to Mike the Mad Biologist.
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