I'm heavily struggling in learning simple and basic probabilistic modeling. So I'm learning probability from this probability book Introduction to Probability by Dimitri P. Bertsekas.
Although I understand the theory but when I do the exercises (even the ones in the chapter not at the end of the chapter) I almost always fail to solve them. So for example, I understand the idea of Bayes' rule but then when I face a problem that i have to solve (i.e model it from text into equations) I almost always fail.
The problem I'm facing in learning probabilistic modeling is that I can't find a way to assess how correct my modeling/approach is. For example, if when try to solve an equation in linear algebra you can make sure that your solution is correct by plugging the solutions of the variables into the equation and check if it's correct. However, with probabilities I can't find a way to assess my solution. So I usually end up with a solution at the end of the problem and say "yeah that makes sense". But then when I check the solutions from the authors everything turns out to be wrong.
My questions to you:
1- How should I practice probabilistic modeling? As I said, I understand the theory but I almost always fail when I have to solve a real exercise that involves a problem description that needs to be translated into equations.
2- Is there a way to make sure that my process/solution is correct before consulting the solutions from the authors? Because usually they provide the complete solution to the problem not just the final answers. Actually sometimes even if they simply provide only the final answers you can get a clue of how to solve the problem. Or even I end up just trying with solution strategies until I get a number similar to the solution given by the authors. So I don't end up learning why I should have chosen that approach but rather just used a brute-force way to find the answer.
Edit:
I don't know if anyone here has read that book, but when the authors are explaining an idea and then they give an example, they often omit how they thought about the problem to end up with that modeling. I'm not sure if all probability books are like that, but I would have really appreciated seeing how the authors reached that modeling/solution. So what I would assume is that if you are going to explain how to model a problem using a tree structure, then be consistent and show how you would use a tree structure to solve the examples.
Moving from probability theory to the application of the theory is often difficult. If the application is at all realistic, you usually have to make assumptions that may not be explicitly stated, to think carefully about what parts of the real-life situations involve probability and which don't, and to try to understand the exact role that probability theory can play in answering the question. Unlike many other parts of mathematics, understanding the theory is necessary, but not enough to make a probability model of a real-life situation.
But making sure you do understand the theory really helps. If there are trivial-looking drill examples or exercises illustrating the theory, don't skip them.
Practice really helps. Each time you succeed in doing an applied problem, you learn something about the thought processes necessary to do other applied problems.
Plunging into the problems at the end of the chapter without working your way through the chapter first, then hoping the right equation will jump off the page to rescue you...that almost never helps.
All that said, your question is very vaguely stated. It is easier to give help on a specific problem than to answer a general 'not getting anywhere' complaint. Maybe your instructor can help you through a few problems and then have you do some similar ones, followed by some related, but not so similar ones.
Maybe you can put a few carefully chosen problems on this site, being very clear what theoretical ideas you think might be related, what you have tried already, and what aspects are particularly puzzling to you. Sometimes you may get snarky comments, and sometimes you may just get the answer with no helpful information, and sometimes you may get help from someone who understands just what is bothering you.
Sometimes students come to me the third or fourth week of the term and say they haven't understood anything I have said so far. In these cases, I can offer sympathy and apology, but not much help. Usually, I ask them to find the first thing they did not understand. With something specific to discuss, it is often possible to be really helpful.