Proving Probability Theory: A Guide

[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.

 

[tacman]

Hello cellular,

Thank you for your post and interest in probability theory. Proving probability theory relies on mathematical logic and reasoning. The basic way to prove probability theory is through the use of axioms and theorems. Axioms are statements that are accepted as true without proof, while theorems are statements that can be proven from axioms.

One of the fundamental axioms of probability theory is the Principle of Counting, which states that the probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. This can be used to calculate the probability of a specific situation occurring, given a set of events.

To prove that a situation is influenced by a previous situation, one can use the concept of conditional probability. This is the probability of an event occurring given that another event has already occurred. It can be calculated using the formula P(A|B) = P(A ∩ B) / P(B), where P(A|B) is the conditional probability of event A given event B, P(A ∩ B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

In terms of calculating the probability of a determinate situation occurring after n passes, one can use the concept of independent events. This means that the outcome of one event does not affect the outcome of another event. In this case, the probability of the determinate situation occurring after n passes would be the product of the individual probabilities of each pass.

Overall, the logic behind probability theory relies on the use of axioms, theorems, and mathematical formulas to prove and calculate probabilities. I hope this helps to clarify the basic approach to proving probability theory. Best of luck with your studies!