Probability Puzzle

Here's something to think about.

Imagine you're in a gameshow. You are presented with three doors. Behind one of them is a brand new car. Behind the other two are.... goats. Of course, you are not told where the car is. You need to choose one of the doors, and you get to keep whatever that's behind the door you choose. Unless you're into beastiality, your aim is obviously to win the car.

Let's say you choose the middle one. What's the probability that your choice will win you the car? Right. 1/3.

Now suppose the game takes a turn. Let's say the host doesn't open the door of your choice, but instead he opens another door that he knows will reveal a goat.

And then the host says to you, "Do you want to change your choice?"

(That means, "do you want to switch from choosing the middle door to choosing the left door?")

Should you take that offer?

Now there are two doors left. One might think that the probability is now 50-50. So the natural instinct would be that it doesn't matter whether you switched your choice or not -- choosing either door has the same probability of winning the car.

But you'd be wrong.

Whoever stumble upon my blog and manage to tell me why gets a cookie from me.