Untitled

I read an excellent book a while ago called The Curious Incident of the Dog in the Night-time[Image removed], which has between its covers a lot of interesting puzzles and trivia---mostly dealing with math.

Math is not my subject. I understand it reasonably well, but if we were at a party together I doubt very much we’d shake hands. It’s probably because of this that I didn’t really understand this insane bit of “probability” until last week, when I discussed it with my mother.

The book can set it up better than I, so here, in Mark Haddon’s words, is the problem:

You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. he says that there is a car behind one of the doors and there are goats behind the other two doors. He asks you to pick a door. You pick a door but the door is not openend. Then the game show host opens one of the doors you didn’t pick to show a goat (because he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?

Now the answer, surprisingly enough, is that you should always switch doors. It’s not a 50-50 scenario as you might think.

What baffled me is this: if you boil it down, there are two doors. There is a car behind one of them, and not behind the other…and nothing else has really changed.

The book explains things with numbers, equations, and charts, but for me to understand things (for some reason) I have to be able to really grasp them in my mind. To the endless frustration of my teachers and classmates, I could never really live with a concept if I didn’t know it in my mind.

But I just figured it out. Here’s how I had to look at it:

For changing doors to be the wrong decision, you had to have already picked the car. And there was only a 1/3 chance of picking the car before a goat is exposed.

That’s it. Why did that take me two months?