What is the best way to study Probability? Nowadays, I am studying probability. I want to be an actuary and the first exam that I have to pass is P exam. I just want to know what is the best way and if you can recommend any books please let me know.
Free ebooks would be more preferable.
 A: Introduction to Mathematical Statistics by Hogg & Craig.
A: In my experience, different actuarial exams from various societies
and in various countries can stress quite different topics. Most junior and senior level courses at major universities cover the necessary topics, but unless they are part of a pre-actuarial program, these courses do not always put primary emphasis on what you may find on an exam. 
Because you are already 'studying probability' I think your best
strategy is to look at sample questions from old exams of the society of most relevant to your personal career. As you go along, note
similarities between your current study topics and topics on exams.
Also, be sure you know the exam rules, particularly the policy on
calculators (and types of calculators), and try practice problems under the same conditions as for the exam. 
I know of no actuarial exams that take a measure-theoretic approach to probability. If your current study is pre-measure theory, fine.
If you are taking a measure theoretic approach in your study, then
be sure to pay attention to the non-measure theoretic approaches
and topics that are likely be on your exam (as represented in
sample questions).
Finally, I have to say that the book by Hogg and Craig (some down-votes just now notwithstanding) would be an excellent choice. I believe
both authors have had experience with actuarial curricula. The book
does not use measure theory and is one of the most comprehensive on relevant topics. (I'd be surprised if other equally good books at about the
same level don't get mentioned here as well.)
Addendum: For self study, there is absolutely no reason to get the latest edition of any of the major probability books. Used copies of the current edition of Hogg/Craig are listed online for about $40, and undoubtedly lower prices are to be found for prior editions. Often the only differences between editions are trivial and superficial--or have to do with computational methods that are likely irrelevant for purposes of an actuarial exam. (I would stay away from books offered free on the Internet unless you have the guidance of someone knowledgeable. Some pretty good, some quirky as to coverage and/or
full of mistakes.)
