Math 20. Discrete Probability

Summer 2009


Office hours from 1pm to 5pm on Thursday and Friday.

To practice for the final I suggest trying out the earlier homeworks, midterms and exercises from 5.1 (this is useful because it doesn't mention which distribution to use, so it helps in practicing figuring out the distribution just like in a test). Section 11.2 has a lot of good exercises and I will likely grab a problem from this section (as I like it a lot). If you want to know if you are solving the problems correctly, feel free to email me or come to office hours (I will hold office hours on Tuesday, Wednesday and Friday in the afternoon).

Homework 8 is due on Wednesday August 26, 2009 (note that Homework 7 is due the same day, homework 8 is meant to represent class on Friday):
Section 11.3: 1,2,3, 6, 24

Homework 7 is due on Wednesday August 26, 2009:
Section 11.1: 2, 4, 8, 11, 19
Section 11.2: 2, 4, 6, 8, 9, 13, 15

Here's the solution to the fifth homework set
I won't post solutions for the fourth homework set, if you have any questions about that homework, just email me.

Here's the solution to the Practice Exam

Solutions to the third homework set can be read here

Solutions to the first homework set found here
Solutions to the second homework set found here

The midterms have been scheduled: July 20, 2009 from 5pm-7pm at room 008. August 10, 2009 from 5pm to 7pm at room 008.

The final exam is Sunday August 30, 2009 at 8am. Room to be announced


Introduction to Probability (2nd revised edition) by Charles M. Grinstead and J. Laurie Snell

This book is available at Wheelock Books for $50, and also may be downloaded from

Tentative syllabus

This syllabus is subject to change, but it should give you an idea of the topics we will cover.


Sections in the textbook

Brief Description

Week 1 1.2, 3.1 Basic probability. Combinatorics: permutations.
Week 2 3.2, 4.1 Combinations. Conditional probability.
Week 3 6.1, 6.2 Expected value. Variance.
Week 4 5.1 Midterm 1. Important distributions.
Week 5 8.1 Law of large numbers.
Week 6 9.1 Central Limit Theorem: Bernoulli trials
Week 7 9.2
Central Limit Theorem: Independent trials. Midterm 2.
Week 8 11.1, 11.2 Introduction to Markov chains. Absorbing Markov chains.
Week 9 11.3 Regular Markov chains, ergodic Markov chains
Besides these topics there will be Bonus Lectures given on x-hours about Probability Gems such as Card Shuffling (Chapter 3.3). The bonus lectures will be for students that want to learn extra stuff not covered in the exams.


The course grade will be based on:
Homework 15%,
Midterm 1 25% ,
Midterm 2 25% and
Final Exam 35%.


There will be homework due roughly every week. It will consist typically of a reading assignment (of the part of the book covered in class) and some problems. Collaboration in the homework is permitted, but you are not allowed to copy someone else's work. The solutions must be written individually. You have to mention on your problem set the names of the students that you worked with.


On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams.

The first midterm will be on Monday July 20, 2009 from 5pm to 7pm in Kemeny 008

The second midterm will be on Monday August 10, 2009 from 5pm to 7pm in Kemeny 008

The final exam will be on Sunday August 30, 2009 from 8am to 11am Room TBA

Students with disabilities: Students with learning, physical, or psychiatric disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see me before the end of the second week of the term. All discussions will remain confidential, although the Student Disability Services office may be consulted to discuss appropriate implementation of any accommodation requested.

Honor Principle

A recap of what is stated above. On homeworks, collaboration is permitted, but each student writes his/her own solutions.
In the midterms and exams, No collaboration is permitted.

Last modified on June 26, 2009.