# What is the best book to learn probability?

Question is quite straight... I'm not very good in this subject but need to understand at a good level.

• what do you mean by probability and to what level do you need it? Apr 9, 2011 at 3:06
• I meant a statistics subject and I want a level that make easier to do exams. The books I have always gaps on explanations and that's make me crazy... Apr 9, 2011 at 3:23
• As noted, there are different sorts of "probability". (1) a branch of finite combinatorics (2) assuming knowledge of Riemann integral (maybe even Riemann-Stieltjes integral) (3) presupposing measure theory. Answerers should explain which of these they are talking about. Apr 9, 2011 at 14:10
• @GEdgar: yes, but even more the questioner should make more precise what he is looking for. It is very inefficient and a waste of people's time to ask for a spray of all possible answers. In fact I think this is as yet not a real question and I am voting to close... Apr 11, 2011 at 6:02
• @pete-l-clark oh cum man! I believe you're in a bad day. I asked a question because I don't know anything about the subject if I knew how to be more precise I wouldn’t ask THIS question which is very clear and simple. Thanks @GEdgar for your viewpoint, together with @wnoise and @PEV I can now form some strategy to START SOMETHING - and that's is all what I need for the moment. Cheers, mate!! May 3, 2011 at 20:07

For probability theory as probability theory (rather than normed measure theory ala Kolmogorov) I'm quite partial to Jaynes's Probability Theory: The Logic of Science. It's fantastic at building intuition behind the rules and operations. That said, this has the downside of creating fanatics who think they know all there is to know about probability theory.

• What are readers of this book missing in their understanding of probability theory? Jun 24, 2016 at 0:17
• @Hatshepsut: On the probability side proper, rigorous handling of infinities that don't derive from limiting trends of finite cases, (e.g. measure theory, Borel subalgebras, and all that goodness). It also doesn't cover in any depth several applications that are generally treated as standard, such as Markov chains, random walks, characteristic functions, etc. It certainly doesn't cover enough to say, prepare for a course on stochastic differential equations. Jun 24, 2016 at 20:47
• Just from the introduction the author claims himself as a partisan of Bayesianism and supports Kline against Bourbaki. Is there something to read for the "other side" of these lines? Apr 14, 2020 at 1:31

A First Course in Probability by Sheldon Ross is good.

• I second this, and would like to mention "Probability Theory: A Concise Course" by Y.A. Rozanov May 4, 2015 at 1:02
• There is also Introduction to probability models by Ross. Out of the two Ross books which one would you recommend for better understanding and problem-solving skills? I know this is from long ago but if someone could answer it would be helpful. Aug 14, 2020 at 1:17
• @Kurapika I'm working through "First Course". There are some questions in there that are quite difficult, so I think this book is more targeted toward an advanced undergraduate. I haven't looked at the Probability Models book, though I would presume it has a lot of overlap with First Course. Jan 25, 2021 at 1:06
• @Kurapika I took a quick look at both books. Seems the "Models" book is more oriented towards teaching probability for application in engineering, while "First Course" is more 'pure probability'. More precisely, "First Course" seems to be more rigorous, while "Models" seems to cover more ground in roughly the same amount of pages, e.g., including Markov chains. In the Applied Mathematics bachelor in my university, "Models" is used.
– Henk
May 4, 2021 at 9:16

If anybody asks for a recommendation for an introductory probability book, then my suggestion would be the book by Henk Tijms, Understanding Probability, second edition, Cambridge University Press, 2007. This book first explains the basic ideas and concepts of probability through the use of motivating real-world examples before presenting the theory in a very clear way. I found a nice feature of the book the fact that simulation is deliberately used to develop probabilistic intuition. The book also discusses more advanced topics you will not easily find in other introductory probability books. The more advanced topics include Kelly betting, random walks, and Brownian motion, Benford's law, and absorbing Markov chains for success runs. Another asset of the book is a great introduction to Bayesian inference.

I wouldn't know which book is the best, because I've only used two when I was taking a course in probability, but if you'd prefer videos , I'd suggest:

MIT 6.041SC Probabilistic Systems Analysis and Applied Probability course , which is available in MIT OpenCoursWare for free :

• Wow, thank you so much for this! This professor is very good and clear :)
– Ovi
May 31, 2017 at 0:30

Here is a list of great books to own to learn probability & statistics. Some on the list like programming in R are great add-on stuff to know.

While not a book, Sal Khan's site: http://www.khanacademy.org/ offers dozens of short videos that provide introductions to probability and statistics. Many of the videos even have problem sets associated with them. Khan provides accessible and often intuitive explanations.

He also has extensive video lessons on algebra, linear algebra, calculus, and geometry as well as physics.

Find a discussion on this forum which explores pro's and con's about Khan at:

What does Khan Academy have to offer? Depth? Rigor?

I happened to take an introductory course on probability and statistics on two different universities. In one they used a horrible book, and in the other they used a truly amazing one. It's rare that a book really stands out as fantastic, but it did.

Probability and Statistics for Engineers and Scientists by Ronald E. Walpole, Raymond Myers, Sharon L. Myers and Keying E. Ye.

The version number doesn't matter, just find an old version second hand.

It is really thorough, takes one definition at a time, and builds on top of that. The structuring and writing is top class, and the examples are well chosen.

Don't worry if you are not an engineer. When using examples they have taken them from the domain of engineering, eg "A factory produces so and so many items per hour, and only so and so many can be broken, ...", instead of using examples from fx social science or economics. But they don't involve engineering science such as statics, aerodynamics, electronics, thermodynamics or any such things. This means that everyone can understand the book, it does not even help to have an engineering background. Perhaps the examples are more appealing/interesting to engineers, but that's all.

• I've used this book briefly. It is quite 'mathematical' for a book aimed at engineering students, but it's more oriented towards application than a pure maths text would be. Can recommend!
– Henk
May 4, 2021 at 9:21

An Introduction to Probability and Random Processes by Kenneth Baclawski and Gian-Carlo Rota is very good, though it does require the reader to have or develop mathematical maturity.

The best book that I have ever read for undergrad and grad students is Intuitive Probability and Random Processes Using MATLAB.

"Lectures on probability theory and mathematical statistics" by M. Taboga. While pretty elementary, it provides proofs of all the main results in probability theory, something you would not find in most other elementary textbooks. It also has plenty of solved exercises and examples. There is a free digital version of this book available at https://www.statlect.com

I found that nobody has pointed out Joe Blitzstein's fantastic book and lectures. the lectures are intuitive and professor Blitzstein does a really good job of explaining the causes behind certain phenomenons in probability, not just mentioning the phenomenon itself, like why do we care about specific distributions, what is the interpretation of a number between 0 and 1 as a probability. he also provides context to each problem for example he mentions how the problem arose? was it a historical problem about gambling or was it a computer science problem or an information theoric one or...?

you can find both the book and lectures in here.