Description: This course covers basic probability techniques including dependent and independent events, compound probability, complementary probabilities, and casework. We’ll also introduce more advanced counting topics such as utilizing symmetries and recognizing distinguishability. We’ll see how we can use geometry to solve probability problems, and we’ll explore more combinatorial identities in Pascal’s triangle including the Hockey Stick Identity and the Binomial Theorem.
- Week 1 – Basic Probability Techniques
- Week 2 – Compound Probability, Complementary Probabilities
- Week 3 – Casework and Probability
- Week 4 – Counting with Symmetries
- Week 5 – Distinguishability
- Week 6 – Geometric Probability Mixed Review
- Week 7 – Expected Value
- Week 8 – Hockey Stick Identity
- Week 9 – Binomial Theorem
- Week 10 – Mixed Review
Homework: Math is not a spectator sport. Practice is essential, hence twenty to thirty minutes of homework three times a week and a desire to improve will be the key to getting the most out of this course.
Prerequisites: Probability is just a ratio of two counting problems; therefore, students should have experience with various counting techniques including permutations and combinations. This class is intended to be follow-up to ECAE’s Introduction to Counting class offered in the fall. Students should be advanced in mathematical reasoning beyond grade level and must be fluent with basic pre-algebra skills such as fractions, decimals, percents, and ratios. Algebra is not a prerequisite, but students should have some experience solving basic linear equations and working with square roots and exponents.
Pre-Test: Students should be able to correctly answer 90% of the problems in the pre-test before beginning this class.
Post-test: Students who can answer most or all of the questions on this post-test will likely find this course mostly review.
Instructor: Jolene Gleason