A Probability Quiz

Clap clap clap...

And here you are... in the final stage of the most popular quiz in the world: "Where is the key?" (I made up the name in 5 seconds).

Ok, here is the situation. You have beaten all other contenders. Now they put 3 boxes in the front of you. One of them contain a dream vehicle's key that you always wanted. The other two is empty. Here's the deal: If you can guess which box contain the key then the key is yours (I'm not sure about the car but that's not the point). First you choose box number one. The quiz guy smirks. He (with the knowledge of what inside every boxes) removes box number two and he said that there's nothing in it, and yes, he's quite honest guy. Furthermore, out of his generosity, he offers you another chance. Whether it's to choose the box number one or box number three. You, being in the front of ten thousand audience, have to choose. What will you do?

This is a game of probability. Perhaps most of you realized that from the beginning. However, not all of us capable of calculating the correct probability of getting the right box (including me).

1. A spectator in front line doing his mathematic: he said that it doesn't really matter which box you choose. Because box number one and box number three have the same probability, which is a half.
2. A smart looking kid has a different perspective. At first, the three boxes have the same probability: 1/3. It means that you have a third chance of winning and a two third chance of failing. One of the other box, which is said to be empty, is removed. Removing one of the the box doesn't really affect your probability of winning. However, by removing one of the box and giving you another chance then you will have a better probability of winning by changing your choice.

As you probably can guess, a smart looking kid is no ordinary kid. By changing decision you actually have a probability of 2/3 to get the key. You don't believe it? Why don't you try it by yourself?