# Chapter 1: Independent and Dependent Events

## Introduction

Probability is present in many parts of our everyday lives. When you say it is raining and your numbers came up in the lottery, you are talking about 2 independent events. The fact that it is raining is not dependent on the fact that your numbers came up in the lottery, and vice versa. If you say that you have the flu and you are taking medicine, you are talking about dependent events. The terms independent and dependent in mathematics are the same as those found in the English language. In order to determine probabilities mathematically, we need to understand the differences between the definitions of independent and dependent. Independent events are those where the outcome of one event is not affected by the other, and dependent events are events where the outcome of one is affected by the other. Other terms, such as mutually inclusive and mutually exclusive, are also important. With mutually inclusive events, the concept of double counting is taken into account in the calculation of probabilities when using the Addition Principle.

## Chapter Outline

- 1.1. Venn Diagrams
- 1.2. Independent Events and Sample Spaces
- 1.3. Dependent Events and Sample Spaces
- 1.4. Mutually Exclusive Events
- 1.5. Mutually Inclusive Events

### Chapter Summary

## Summary

This chapter covers how events can be diagrammed and organized. It starts with how to draw Venn diagrams, and why they are used. It goes on to cover the distinction of independent and dependent events, and how the Multiplication Rule can be used to solve for probabilities in finite sample spaces. Lastly, it covers mutually inclusive and exclusive events, how to represent those with Venn diagrams, and how to calculate their probabilities.