## Saturday, August 20, 2005

### Game Show

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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors?

1. Good answer. But I was thinking of not just losing out, but gaining!

2. This question was asked by Craig Whitaker in the "Ask Marilyn" in Parade Magazine in 1996. Marilyn's answer got quite a backlash, but it turns out she got it right.
If you switch to the other door, instead of having a 1 in 3 chance of winning, you'll have a 2 in 3 chance! The idea is simple but quite counterintuitive. By making a "blind" choice between the three doors, you have a 1 in 3 chance of being right, but a 2 in 3 chance of being wrong. Then door 3 is removed. By switching away from your first choice to door 2, you'll now have a 2 in 3 chance of being right!

3. If you'd like to try out this answer in an interactive way, use cards instead of doors. Always switch away from your first choice. If you keep track of how many times you get the "prize", you'll see soon enough that Marilyn got it right!

You might also try searching on the web for the "Monty Hall" problem.

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