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The best introductory book I've read is Chance in Biology: Using Probability to Explore Nature by Mark Denny and Steven Gaines. While most introductory books have mainly examples from games of chance, this book uses examples from physics, chemistry and biology. It's very accessible and it takes you very fast from the basic rules of probability theory to useful examples.
I would also recommend Jaynes' lectures. They're more informal than the book (and also free :D). These I think are the best for quickly understanding the "subjectivist" approach to probability theory.
It's not "blatantly false". To get from theory to practice you have to add to the theory various pieces of information about the practical issue. E.g. you might have a general theory of economics, but as a businessman you also have to consider the local details (which are not part of the general theory).
The general theory might tell you (in the best case scenario) what information you need to gather (e.g. Newtonian mechanics tells you that in order to solve specific problems you have to know the force and measure position and velocity at a given time), but even so, you still need to gather that information. So the relationship between theory and practice is not reversible: you may have a general theory and yet be unable to solve specific problems (as you lack the specific information - e.g. meteorology), or you may be able to solve specific problems but lack a general theory (e.g. psychology).
"What can be asserted without evidence can also be dismissed without evidence." Christopher Hitchens