## Probability treatments in introductory textbooks, popular books and Wikipedia

I am a firm believer in the policy
never write an explanation of something which has already been explained well (at comparable length and level of sophistication)
though my experience as reviewer of popular books shows that few authors share this belief. As background to my program of articulating what Probability says about the real world, I have paid attention to what's already out there. This page provides a summary.

Textbook "an introduction to mathematical probability" accounts exist at every level from elementary school to College junior level. At the latter end, typical contents in a post-calculus text are

• Jargon: events, sample space, random variables.
• The basic mathematics: expectation, independence, addition and multiplication rules; illustrated via games of chance.
• Law of large numbers, central limit theorem.
• Named distributions and prototypical settings where they appear.
• Calculus-style manipulations with random variables and distributions.
• Conditional probability and Bayes rule.
• Correlation and regression.
More elementary courses just cut out some of these topics. My point is that such books are organized by intrinsic mathematical structure. They show how the different mathematical ingredients are related, but real-world uses form only a small and scattered part. More discussion is on my what probability textbooks don't tell you page.

Wikipedia's (often overlooked) page List of probability topics shows the breadth of Wikipedia's coverage. Being an encyclopedia, this consists of articles which are each focussed on one topic, typically a mathematical concept. These are valuable in many ways, in particular as a reference for definitions and history. But the encyclopedia style does not allow discursive writing or judgements of what is significant or interesting or non-trivial.

Popular science books have a range of styles but with many commonalities. See this page for my reviews of around 100 such books. Almost all describe some parts of the history of probability, along with the some associated basic mathematics -- laws of large numbers and normal approximation -- and uses in games of chance. Most such books also sample from a menu of cute elementary math calculations or paradoxes, such as the following. Ironically these are usually better explained on Wikipedia.

The cover blurb of a popular science book invariably talks about the breadth of real-world applications of probability. I have never seen any serious attempt at a comprehensive list of fields of application, to use as a reference, so am creating my own as A map of the world of chance. The actual breadth of some popular science books (and other writings) can be seen, with reference to that list, at this page. (xxx on web).

Finally I confess to a guilty pleasure, making fun of an elderly philosopher's examples of luck in everyday life, many of which are better described as "notes for a historical romance-adventure novel".