Every theory has its successes, and its limitations. These notes are about the successes of probability theory. But it doesn't hurt to explain in non-technical language some of its limitations up front. This way the reader can understand the basic premise before investing considerable time.
To begin with, we start with a truism. Real world is complicated, often to a larger degree than scientists will readily admit. Most real phenomena have multi-aspect form, and can be approached in multiple ways. Various questions can be asked. Even seemingly the same question can be answered on many incompatible levels. For instance, the generic question about dinosaur extinction has the following variants.
Theses questions are ordered from the most individual level to the most abstract. The reader should be aware that probability theory, and stochastic modelling deal only with the most abstract levels of the question. Thus, a stochastic model may perhaps shed some light whether dinosaurs had to go extinct, or whether mammals will go extinct, but it wouldn't go into details of which comet had to be responsible for dinosaurs, or which is the one that will be responsible for the extinction of mammals.
It isn't our contention that individual questions have no merit. They do, and perhaps they are as important as the general theories. For example, a detective investigating the cause of a mysterious death of a young woman, will have little interest in the ``abstract statistical fact" that all humans eventually die anyhow. But individual questions are as many as the trees in the forest, and we don't want to overlook the forest, either.
Probabilistic models deal with general laws, not individual histories. Their predictions are on the same level, too. To come back to our motivating example, even if a stochastic model did predict the extinction of dinosaurs (eventually), it would not say that it had to happen at the time when it actually happened, some 60 million years ago. And the more concrete a question is posed, say if we want to know when Dino the dinosaur died, the less can be extracted from the stochastic model.
On the other hand, many concepts of modern science are define in statistical, or probabilistic sense.(If you think this isn't true, ask yourself how many trees do make a forest.) Such concepts are best studied from the probabilistic perspective. An extreme view is to consider everything random, deterministic models being just approximations that work for small levels of noise.