I have taken a course in probability and statistics, and did well, but still I feel that I do not grasp the core of what holds the theory together. It is a little weird that I should use a lot of theory when I do not get the simple building block of the theory. I am basically wondering if probability is defined in some way? In the statistics books I have looked in, probability is not defined, but at the beginning of the book, they give a describtion of how we can look at probability, and this is usually the relative frequency model, but they never define it to be this? These steps is what I seem to see in a statistics books, do they seem fair? 1. Probability is described in terms of events, outcomes and relative frequency, but never defined. 2. A lot of theory is then built regarding probability. 3. Then with the help of Chebychevs inequality, we are able to show that the relative frequency model is correct. That is, if the probability for an event is p, and X is a bernoulli random variable, then mean(X) will converge to p. Do you see my problem? If we say that the probability for an event is p, then we can show that the relative frequency of the of the event in the long run is p. In order to show this, we used all the theory of linear combinations, variance etc.. But this means that the relative frequency model is a consequence of our theory, correct? I mean, we can not say that the probability is the relative frequency, then develeop a lot of theory, and then prove that p equals the relative frequency, then we are going in a circle?