# Recommendations for free, basic resource on discrete probability for a discrete structures class?

I'm teaching a course this fall on Discrete Structures for Computer Science. It's taught out of the math department but is a service course for the CS department with 90-95% of students being CS majors. I've taught the course before a few times, and this fall we are introducing a content unit on discrete probability that hasn't been there before. The other content units cover sets, counting, logic, and proof. Discrete probability will come last, after all the other stuff is covered.

The problem is that the book I'm using doesn't have any discrete probability in it. Which isn't really a problem as long as I can find a good, free online supplement for students to use. The learning outcomes for this unit are:

1. Calculate probabilities of events and expectations of random variables for elementary problems such as games of chance.
2. Differentiate between dependent and independent events.
3. Identify a case of the binomial distribution and compute a probability using that distribution.
4. Apply Bayes' theorem to determine conditional probabilities in a problem.
5. Compute the variance for a given probability distribution.
6. Explain how events that are independent can be conditionally dependent and identify real world examples of such cases.

Those learning outcomes are taken from the ACM recommendations for discrete probability, in discrete math courses for CS majors.

A brief Google search brings up a ton of free books and video resources that are way too high of a level for the course -- as in, graduate-level stuff whereas this course is mainly second-year CS majors with minimal math backgrounds. The closest match I found was this wikibook but it doesn't seem to cover all the bases. So I'm wondering if you've got anything to share. Thanks in advance.

There is Grinstead & Snell's Introduction to Probability, Second Revised Edition. It is freely available under GNU Free Documentation License, as explained on the linked page. The level is undergraduate and the authors state in the preface:

The text can also be used in a discrete probability course. The material has been organized in such a way that the discrete and continuous probability discussions are presented in a separate, but parallel, manner.

Have you looked at Khan Academy? They seem to cover just about all of this in their video lectures and follow it up with exercises to mastery. Students can have you as their "coach" and you can assign those exercises that you think are helpful. I've used it with elementary - high school students and they have all found it useful. I assume you would supplement with your own teaching.

I recommend examining the site Seeing Theory to see whether it suits your needs.

There is a corresponding text draft (link) on which the authors are actively seeking feedback.

It is a free, basic resource that covers some of the topics that you list, and perhaps can be useful in other ways, too. From my casual perusing of the site, it seems quite well-constructed/organized.

It sounds like a very basic, short survey of conventional prob/stat ("probes and shafts"). But it's not clear to me that "discreteness" should be a limiter rather than a simple overall prob/stat unit...but your call on that. You want the basics so that students can do school projects using the concepts of standard deviation, etc. Also, stats is more and more a thing in the every day information worker business world, so helps them with coops, etc. And of course, stay the heck away from crazy hard measure theory grad student math stuff. The kids need to know how to use some basic stats tools, not to prove how they were derived.

Couple ideas:

1. Take a look at the single chapter in Lindeberg's EIT/FE reference manual (your library should have it). It covers the key topics (and does so very efficiently) within 11 pages (at least in the eighth edition). You could just use it as some guidance and write some ppt slides to summarize the information. Or you could pl... ;-)

2. Came up with this from a quick Google search, looking for Six Sigma prob/stat review: http://www.qualitiamo.com/documenti/prob-stats-review.pdf [It is pretty short and action oriented. But it is basically all stats, lacking the permutations and combinations. Personally I like perm/combinations, but distributions are more relevant to job type tasks. You would need to supplement it a little or just bail on the games of chance objective.]