# Lesson 2: Properties of Probability

### Introduction

#### In this lesson, we learn the fundamental concepts of probability. It is this lesson that will allow us to start putting our first tools into our new probability toolbox.

### Objectives

In this lesson, we will:

- Learn why an understanding of probability is so critically important to the advancement of most kinds of scientific research.
- Learn the definition of an event.
- Learn how to derive new events by taking subsets, unions, intersections, and/or complements of already existing events.
- Learn the definitions of specific kinds of events, namely empty events, mutually exclusive (or disjoint) events, and exhaustive events.
- Learn the formal definition of probability.
- Learn three ways — the person opinion approach, the relative frequency approach, and the classical approach — of assigning a probability to an event.
- Learn five fundamental theorems, which when applied, allow us to determine probabilities of various events.
- Get lots of practice calculating probabilities of various events.