# 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

Sets and groups are descriptive terms used in algebra for a collection of any items or elements. Learn about the definition of sets and groups, numerical sets, group operations, group rules through a series of examples.

### 2. Recognizing Power Sets in Algebra

From apples to zebras, in algebra, a set can be defined as a collection of items, while a power set contains all of the possible subsets to a given set. Learn how to define and write sets, subsets, and power sets in algebra, determine how many subsets are in a given power set, and discover how to recognize them.

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

In math, set notation defines the criteria and properties of a set using symbols. Learn what set notation is, explore set notation with numbers, and discover how to write sets using set builder notation.

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

Mathematical sets are collections of objects or concepts that can be joined together to become mathematical building blocks. Learn about mathematical sets and understand their function in mathematics. Explore the roles of elements, intersections, and unions in mathematical sets.

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

Events can be viewed as subsets of a sample space or the result of all possible outcomes of an experiment. Learn about the definition, explanation, and real-world examples of events, subsets, and sample spaces.

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

Probability can be calculated for simple, compound, and complementary events. Explore each type of event, understand how each event differs from the other types, and learn how to calculate each type of event's probability by reviewing examples.

### 7. Probability of Independent and Dependent Events

Probability is a ratio that predicts the likelihood an event will occur. Explore the concept of probability and understand the difference between independent and dependent events. Learn how to calculate the probability of both independent and dependent events, and review examples.

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### Other Chapters

Other chapters within the Honors Precalculus Textbook course

- Working with Linear Equations
- Working With Inequalities Review
- Absolute Value Equations Review
- Working with Complex Numbers Review
- 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 & Conic Sections Review
- Polar Coordinates and Parameterizations
- Working with Sequences & Series
- Continuity
- Limits in Precalculus