This is the main navigation page for Unit 2 of the course Introduction to Statistical Analysis, developed using openly licensed materials from Saylor.org's Introduction to Statistics. Below you will find a full description of Unit 2 in general, as well as for each subunit. Follow the links within each subunit description to access particular topics, or proceed directly to the Unit 2 Content Page.

## UNIT 2: PROBABILITY TOPICS

After you've learned to describe and display data, how can you use the sample data to draw conclusions about the populations? To answer this question, you need probability, a subject we will explore over the course of this unit.

If you open a newspaper, you are likely to read headlines like: “Should risky medical procedures be allowed?”; “30% chance of a hurricane this weekend”; “Analysts expect the gas prices to increase this summer”; and “Two brothers meet by accident after being separate for more than 20 years.” All of these topics deal with everyday life and all of them have to do with chance or probability.

The world seems to be full of events that seem unpredictable. Probability theory is a tool that was created to deal with such events more effectively. For example, before getting a surgery, a patient wants to know the chances that the surgery might fail; before taking medication, we want to know the chances that there will be side effects; before leaving our houses, we want to know the chances that it will rain today. Probability deals with the chance of an event occurring. It is a measure of likelihood that takes on values between 0 and 1, inclusive, with 0 representing impossible events and 1 representing certainty and the chances of events occurring fall between these two values. The ability to calculate probability allows us to make better decisions. Probabilities affect our everyday lives.

In this unit, you will learn what probability and its properties are, how probability behaves, and how to calculate and use it. You will study the fundamentals of probability and will work through examples that cover different types of probability problems. These basic probability concepts will provide a foundation for understanding more statistical concepts. You probably already (intuitively) use concepts from probability, but after this unit, you will be able to formally and precisely predict the likelihood of an event occurring given certain constraints.

Whether we are evaluating how likely it is it to get more than 50% of the questions correct on a quiz if you guess randomly; predicting the chance that the next storm will arrive by the end of the week; or exploring the relationship between the number of hours students spend at the gym and their performance on an exam, an understanding of the fundamentals of probability is crucial. Make sure you spend time on this unit. Our goal will be to become comfortable with the basic machinery of probability theory and its applications.

Time Advisory: This unit will take you 6 hours to complete.

### Learning Outcomes

Upon completion of this this unit, you will be able to:

• Understand and use the terminology of probability.
• Determine whether two events are mutually exclusive and whether two events are independent.
• Calculate probabilities using the Addition Rules and Multiplication Rules.
• Construct and interpret Contingency Tables.
• Construct and interpret Venn Diagrams.
• Construct and interpret Tree Diagrams.

### Subunits

Unit two consists of four main topics:

#### Probability Topics and Terminology

This topic will introduce you the major concepts fundamental to probability and the terminology associated with them.

## About the Resources in This Course

This course project draws upon three main types of resources:

The first are readings and video lectures from Barbara Illowsky and Susan Dean’s Collaborative Statistics, which is available freely under a Creative Commons Attribution 2.0 Generic (CC BY 2.0) license from the following location: http://cnx.org/content/col10522/latest/

The second type of resources in this course are lectures from Kahn Academy. These lectures are available under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0) license. Kahn Academy has many lectures available from http://www.khanacademy.org/

Finally, the above resources have been woven together and organized into a format analogous to a traditional college-level course by professional consultants that work as experts within the subject area. This process was facilitated by The Saylor Foundation. Additionally, if you have worked through all of the material contained in this project, you may be interested in taking the final exam provided by Saylor.org or completing other courses available there that are not yet on Wikiversity.