Basic Notions for Finite and Denumerable State Models

Abstract

Let us first discuss the intuitive background of a context in which the probability notion arises before trying to formally set up a probability model. Consider an experiment to be performed. Some event A may or may not occur as a result of the experiment and we are interested in a number P(A) associated with the event A that is to be called the probability of A occurring in the experiment. Let us assume that this experiment can be performed again and again under the same conditions, each repetition independent of the others. Let N be the total number of experiments performed and N _A be the number of times event A occurred in these N performances. If N is large, we would expect the probability P(A) to be close to N _A /N

$$ P(A) \approx {N_A}/N $$

((1))

.