Probability of a random number - seems impossible

[raspberryh]

Hi guys,

I have a question re: random numbers and probability. If I have a random number generator that generates a number between 1 and 10, and say I generate a kazillion of these numbers, then doesn't each number have the same probability of showing up? So then, after a kazillion numbers, I could take the average of all these random numbers I've generated and the average should be 5.

However, these numbers are random. Which means all this stuff just goes out the window basically - right? I mean, the probability that I would get all 9s a kazillion times should be the same as the probability that I get an even distribution of all numbers - right?

And if this is true, then that means if I have a 6-sided die, then the probability that I get the same side every time a kazillion times in a row should be the same as the probability that I can have an even distribution. Because it is random, and you never know with random.

And I know you might say that if we wait until we generate an infinity amount of random numbers, THEN we would have even distribution... however, isn't it possible that you could get 9s infinity times in a row? It must be, because it is random!

Please help. My world is falling apart.

Thanks :)

 

[mathman]

However, these numbers are random. Which means all this stuff just goes out the window basically - right? I mean, the probability that I would get all 9s a kazillion times should be the same as the probability that I get an even distribution of all numbers - right?

Wrong. There is only one way to get all 9s, but there are many ways to get a set of numbers whose average is approximately 5 (law of large numbers).

 

[M-quest]

Mathman is right,getting a kazillion 9s is not equiprobable to getting an even distribution,i.e it can only happen in 1 way while the numbers can be evenly distributed a number of different ways e.g. the probability of 6000 6s in 6000 throws of a die is not even close to being equal to the probability of 1000 1s,2s,3s,4s,5s and 6s.