# Ch 33: Sets & Probability

### About This Chapter

## Sets & Probability - Chapter Summary and Learning Objectives

This chapter can help you focus on learning more about sets and probability. You can survey various kinds of sets and develop your understanding of types of probability. These lessons will help you study:

- The differences between groups and sets
- How to recognize a power set
- Ways of writing set builder notation
- How to identify subsets
- How to measure the probability of simple, compound, complementary, independent and dependent events

Video | Objective |
---|---|

Introduction to Groups and Sets in Algebra | Develop a general understanding of sets. |

Recognizing Power Sets in Algebra | Distinguish the power set of a given set. |

How to Write Sets Using Set Builder Notation | Diagram a set of numbers with the use of set builder notation. |

Mathematical Sets: Elements, Intersections & Unions | Evaluate basic set theory. |

Events as Subsets of a Sample Space: Lesson & Quiz | Focus on understanding and identifying subsets. |

Probability of Simple, Compound and Complementary Events | Assess how to determine the probability of simple, compound and complementary events. |

Probability of Independent and Dependent Events | Learn how to measure the probability of independent and dependent events. |

### 1. Introduction to Groups and Sets in Algebra

As an introduction to the algebraic concepts of sets and groups, this lesson covers the difference between the two concepts and how to determine if a set is a group. To complete this lesson, we'll take a look at some practice examples.

### 2. Recognizing Power Sets in Algebra

This lesson will give students a very brief introduction to sets and subsets as a lead into how to determine if a set is actually a power set. Through the use of examples and trials, students will learn to identify true power sets.

### 3. How to Write Sets Using Set Builder Notation

Set builder notation allows the user to indicate specific items that are to be included within a set. In this lesson, we will learn how to write sets using set builder notation.

### 4. Mathematical Sets: Elements, Intersections & Unions

Today we're going to explore mathematical sets, which are surprisingly simple! Sets are just collections of any objects or concepts, also known as elements, that can be related to each other through union or intersection.

### 5. Events as Subsets of a Sample Space: Definition & Example

Probability can get very confusing at times. You will find that some words, such as events and subsets, are often referring to the same concept depending on the experiment. Use this lesson to understand the concept of events as subsets.

### 6. Probability of Simple, Compound and Complementary Events

Simple, compound, and complementary events are different types of probabilities. Each of these probabilities are calculated in a slightly different fashion. In this lesson, we will look at some real world examples of these different forms of probability.

### 7. Probability of Independent and Dependent Events

Sometimes probabilities need to be calculated when more than one event occurs. These types of compound events are called independent and dependent events. Through this lesson, we will look at some real-world examples of how to calculate these probabilities.

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### Other Chapters

Other chapters within the Honors Precalculus Textbook course

- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling for Precalculus
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Types of Functions in Precalculus
- Understanding Function Operations
- Graphing Functions in Precalculus
- Graph Symmetry
- Rate of Change
- Polynomial Function Basics in Precalculus
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions & Function Graphs in Precalculus
- Exponential Functions & Logarithms in Precalculus
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions in Precalculus
- Vectors in Precalculus
- Matrices and Determinants in Algebra
- Understanding Arithmetic Sequences & Series
- Understanding Geometric Sequences & Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Working with Sequences & Series
- Continuity
- Limits in Precalculus