## STA 12 Introduction to Discrete Probability

**Units:** 4

**Format:**

Lecture: 3 hours

Laboratory: 1 hour

**Catalog Description:**

Random experiments; countable sample spaces; elementary probability axioms; counting formulas; conditional probability; independence; Bayes theorem; expectation; gambling problems; binomial, hypergeometric, Poisson, geometric, negative binomial and multinomial models; limiting distributions; Markov chains. Applications in the social, biological, and engineering sciences.

**Prerequisite:** Two years of high school algebra.

**Goals:
**A great many experiments involve discrete random phenomena that can be modeled and studies in depth without relying on calculus as a tool. Examples included the output from a Geiger counter, the information solicited in any public opinion poll, and variables of interest in many popular games of chance. Statistics 12 introduces the student to the fascination of probability in a course with minimal prerequisites. The course prepares the student for further study in Probability and Statistics, but is primarily intended as a course that will motivate students to want to learn more about the subject. It will lead students to consider taking upper-division sequences such as Statistics 130 or 131.

**Summary of course contents:
**Topics to be covered include: Random experiments; countable sample spaces; elementary probability axioms; counting formulas; conditional probability; independence; Bayes theorem; expectation; gambling problems; binomial, hypergeometric, Poisson, geometric, negative binomial and multinomial models; limiting distributions; Markov chains. Applications in the social, biological, and engineering sciences. Models introduced will be motivated from discussions of real experiments in which these models arise naturally.

**Restrictions:
** None

**Illustrative reading:**

*A Primer in Probability* by Kathleen Subrahmaniam

*According to Hoyle* by Richard L. Frey

*Winning Casino Play* by Avery Cardoza

*An Introduction to Probability Theory and Its Applications* by W. Feller

**GE3:**

SE, QL

**Potential Overlap:**

Statistics 12 is unique in that it treats discrete probability models in a course without a calculus prerequisite. About four week of the courses STA 130A or 131A deal with material in STA 12, but the former courses require two quarters of calculus, and the treatment of this material reflects this prerequisite. In STA 12, only material from 130 or 131 which can be discussed without alluding to the calculus will be presented. There is more time in STA 12 for examples and applications from varied fields. About one fifth of STA 13 also deals with discrete probability models and thus overlaps with STA 12. This material is covered in much greater depth in the latter course.

**History:**

None