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I am currently a junior undergraduate student taking an Introductory Course on Probability Theory. I have been struggling with the subject for the last few weeks because mathematics can be challenging and I haven't built up enough intuition to train my mind to think probabilistically enough.

That being said, I'm between a few choices for a book for supplementary study. I've found the PDFs by Hoel, Port and Stone as well as Hossein-Pishro Nik's online text and Feller Volume 1. I was wondering, which of these books present the material in the most intuitive manner?

I often have a difficult time with Combinatorial Analysis as well, so I'm looking for a book that presents the material intuitively and yet rigorously enough so that I can truly gain a better understanding and grasp of the subject. I am open to any and all recommendations.

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  • $\begingroup$ Introduction to Financial Mathematics by Steven Roman has several chapters purely on probability, and I've found them to be the most intuitive and light, yet formal introduction to this topic. $\endgroup$ – Ilya Sep 4 '18 at 9:55
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My two personal favorites for introductory probability are A First Course in Probability by Ross (there are several editions) and Understanding Probability by Tijms. Neither one uses measure theory. Ross's book is distinguished by its wealth of fully-worked out, interesting examples. Tijms's book strikes me as slightly more modern, with an emphasis on simulation and an unusual structure; the book is in two parts, with the first part an intuitive approach with lots of examples of applications, and the second part more formal.

I like Feller's book, but I don't think it is a good choice for a first introduction. Compared to Ross and Tjims, Feller Volume I is more advanced and doesn't have much discussion of continuous distributions. I can't comment on your other two books because I haven't read them.

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