Testing all the possibilities?

4/26/2006

Have you ever planned to try to test all the possibilities and finally you surrendered?

When you are in high school, there is a lesson in mathematics class to teach you how to count the probability.
The lesson started with something like you need to pick up a red ball inside a black box.
The first thing you need to know is how many balls there, then you need to know how many red balls.
If there are 10 balls and only one red ball, then you will get the result that the probability to pick up a red ball is 1/10.

The lesson will then teach you how to count something more complex.
A similar example is to count the probability that you pick up a red ball and a blue ball from the black box.
If there is totally 10 balls inside the box, only 1 red ball and 1 blue ball. Then the probability is 1/10 * 1/9, which is 1/90.

In the real world, the reason it's so hard to list all the possibilities is due to we may not be able to find all the variables. In mathematics, you can, but in the real world, you can not.