Thursday, August 02, 2007

Math Puzzle: Do You Want To Change Your Mind?

My mom came across this math puzzle recently. I had already seen it and solved it as it was given as a homework assignment in high school senior year in our special math class. Nowadays, it would be difficult to give these kinds of problems as homework, with the Web and Google search.

You are on a game show. There are three doors. Behind one of the doors is the prize of a million dollars. There is nothing behind the other two doors. You get to choose one door to open. If the prize is behind that door, you win. After you choose a door but before it is opened, the game show host opens one of the other doors and shows that it is empty. He then gives you the option to change your mind. Do you go with your first choice, or change your mind?

In other words, what is the probability of winning if you stay with your first choice, and what is the probability of winning if you change your mind?

Any takers?


Lara said...

when you choose, your probability is 2/3 of choosing wrong. thus, to play the odds, you assume you guess wrong. when they show you the the "other" wrong one, you - "knowing" that you have a wrong one - switch to the correct one. i don't remember how to do the math correctly to get the exact probability though.

dancing dragon said...

Thanks for playing. That's pretty much it. I take this as evidence that English majors are actually better at math and logic than a lot of people who study math and science. ;)

Most people seem to answer that the odds of winning are the same, 1/3, or that switching improves the odds to 1/2.

Aditya said...

I agree - always switch. its not as intuitive, but the math works (-:

good morning everyone!!