# Chapter 11: Using Probability

## Introduction

Here you will explore probability in many different ways. To begin, you will be calculating outcomes by using tree diagrams and the Counting Principle. Then you will learn to calculate probability when working with permutations and combinations. This will include evaluating permutations and combinations by using a specific type of notation. Then you will learn how to distinguish between experimental probability and theoretical probability. When you compare multiple events, you will learn the difference between overlapping, disjoint and complementary events. You will learn to calculate odds for or odds against an event happening.Next, you will learn to recognize independent and dependent events. Finally, you will understand conditional probability and geometric probability before using simulations to explore experimental probability.

## Chapter Outline

- 11.1. Using Tree Diagrams
- 11.2. Calculating Outcomes
- 11.3. Recognizing Permutations
- 11.4. Evaluate Permutations using Permutation Notation
- 11.5. Recognizing Combinations
- 11.6. Evaluate Combinations using Combination Notation
- 11.7. Theoretical Probability
- 11.8. Experimental Probability
- 11.9. Write and Compare Probabilities as Fractions, Decimals and Percents
- 11.10. Identify Overlapping, Disjoint, and Complementary Events
- 11.11. Calculate Odds using Outcomes or Probability
- 11.12. Recognize Independent and Dependent Events
- 11.13. Understanding Conditional Probability
- 11.14. Understanding Geometric Probability
- 11.15. Use Simulations to Explore Experimental Probability

### Chapter Summary

## Summary

First, you learned how to define probability and how to calculate outcomes by using tree diagrams and the Counting Principle. Then you learned to distinguish between permutations and combinations. You discovered that when you evaluate a permutation or a combination that special notation is useful and you used factorials in your work.

Next, you learned to identify theoretical probability as distinct from experimental probability. Using this information, you were able to calculate these probabilities in different situations. You learned to write probabilities as fractions, decimals and percents. You learned to calculate odds for or odds against an event happening.

Then you learned about different types of events. These included overlapping, disjoint and complementary events. Venn Diagrams were used too. This lead you to learning about independent and dependent events.

Finally, you learned about conditional probability and geometric probability. You ended with a Concept that focused on exploring experimental probability through simulations.