# Ch 5: Probability: Rules for Events

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### About This Chapter

## Probability: Rules for Events - Chapter Summary and Learning Objectives

The short and fast video lessons in this chapter introduce you to probabilities of different events. You'll learn to calculate probabilities of simple and compound events, independent events and more. These videos teach you how to apply conditional probability to practical situations and use two-way tables. A variety of tools are available with each lesson to aid your study of this topic, including lesson quizzes to check your knowledge of the material, transcripts to pinpoint key terms and video tags to quickly find main points of the videos. These lessons can help you:

- Describe the elements of mathematical sets
- Learn to use read two-way tables
- Link conditional probabilities to independence
- Describe and use the addition and multiplication rules of probability

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

Mathematical Sets: Elements, Intersections & Unions | Determine how unions, intersections and elements work together to create mathematical sets. |

Events as Subsets of a Sample Space: Lesson & Quiz | Describe how events are also considered subsets when you're working with probabilities. |

Probability of Simple, Compound and Complementary Events | Use practical examples to differentiate between these different probability types. |

Probability of Independent and Dependent Events | Differentiate between these two types of probabilities and learn to calculate them. |

Probability of Independent Events: The 'At Least One' Rule | Evaluate the 'at least one' rule and find out how to use it. |

How to Calculate Simple Conditional Probabilities | Get instructions on calculating simple conditional probabilities. |

The Relationship Between Conditional Probabilities & Independence: Lesson & Quiz | Examine how these two concepts are connected. |

Using Two-Way Tables to Evaluate Independence: Lesson & Quiz | Discover how to use a two-way table to evaluate independence. |

Applying Conditional Probability & Independence to Real Life Situations: Lesson & Quiz | Learn how conditional probabilities and independence work in the real world. |

The Addition Rule of Probability: Definition, Examples & Quiz | Use this rule to find probabilities of mutually and non-mutually exclusive events. |

The Multiplication Rule of Probability: Definition, Examples & Quiz | Figure out when you should use the multiplication rule of probability. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. Probability of Independent Events: The 'At Least One' Rule

Occasionally when calculating independent events, it is only important that the event happens once. This is referred to as the 'At Least One' Rule. To calculate this type of problem, we will use the process of complementary events to find the probability of our event occurring at least once.

### 6. How to Calculate Simple Conditional Probabilities

Conditional probability, just like it sounds, is a probability that happens on the condition of a previous event occurring. To calculate conditional probabilities, we must first consider the effects of the previous event on the current event.

### 7. The Relationship Between Conditional Probabilities & Independence

Conditional and independent probabilities are a basic part of learning statistics. It's important that you can understand the similarities and differences between the two as discussed in this lesson.

### 8. Using Two-Way Tables to Evaluate Independence

If you are a visual person, a 2-way table is a great way to analyze information. This lesson shows you how to use a 2-way table to determine the independence of variables.

### 9. Applying Conditional Probability & Independence to Real Life Situations

It can be really confusing learning how to apply conditional and independent probability to real-life situations. This lesson focuses on several examples and practice problems to help you learn how to find conditional probability.

### 10. The Addition Rule of Probability: Definition & Examples

In this lesson, you will learn the differences between mutually exclusive and non-mutually exclusive events and how to find the probabilities of each using the Addition Rule of Probability.

### 11. The Multiplication Rule of Probability: Definition & Examples

The Multiplication Rule of Probability is a concept you will use frequently when solving probability equations. In this lesson, learn the two different scenarios in which you will use the multiplication rule of probability.

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### Other Chapters

Other chapters within the DSST Principles of Statistics: Study Guide & Test Prep course

- Data Types & Measurements in Statistics
- Sampling Methods in Statistics
- Descriptive Statistics of Data Sets
- Visual Representations in Statistics
- Probability Combinations, Permutations & Expected Values
- Probability: Discrete & Continuous Distributions
- Correlation & Regression in Statistics
- Sampling Distributions in Statistics
- Hypothesis Testing in Inferential Statistics
- About the DSST Tests