How Do You Prove Basic Probability Theory?

[serin]

Hello There,
this is my first post. I would like an information: Which is the basic way to prove probability theory?.. I mean prove the probability that a situation in influenzed from the situation before and/or calculate the probability that in n it will have a determinate situation...??
How you see i want the logic.

Bye
P.s This is a problem that derivate from Mathematica of Wolfram and i have to understand how it will be my atom after n (integral number) passes..
Thanks cellular

 

[HallsofIvy]

?? Then pick up an introductory probability text. I'm not going to go through all of that here since "proving that the various probability distributions really do answer the questions they are designed to answer", which is what your question really is,typically takes from 1/4 to 1/3 of an introdutory probability text. Culminating with the "Central Limit Theorem" which basically says "all you really need is the normal distribution"! And I wouldn't pretend to be qualified to give an off hand proof of that.