Ch 4: Probability & Uncertainty

About This Chapter

Utilize this overview of probability and uncertainty to increase your understanding of topics like common probability statements, the multiplication rule of probability, and tree diagrams in math. The lessons in this chapter will help prepare you to take an exam or engage in a class discussion.

Probability & Uncertainty - Chapter Summary

Included in this chapter on probability and uncertainty are lessons on how to calculate simple conditional probabilities, use factorial notation, and determine the number of ways choices can be made from groups. You will also learn to calculate the probability of independent and dependent events. After completing the chapter, you should be able to:

  • Explain events as subsets
  • Use a formula to identify probability
  • Discuss the meaning of common probability statements
  • Explain the difference between mutually exclusive and non-mutually exclusive events
  • Use the multiplication rule of probability
  • Apply independent probability to real life scenarios
  • Describe how tree diagrams work
  • Discuss the probability of simple, compound, and complementary events

Our instructors assist you with quickly grasping the concepts presented. A brief quiz is available to test your understanding after each lesson, and the quizzes can be printed for use as another study tool.

13 Lessons in Chapter 4: Probability & Uncertainty
Test your knowledge with a 30-question chapter practice test
Events as Subsets of a Sample Space: Definition & Example

1. 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.

Introduction to Probability: Formula & Examples

2. Introduction to Probability: Formula & Examples

Ever taken a chance on something? Before you took that chance, did you want to know what your chances were on actually winning? Then you were dealing with probability, the likelihood that a specific event will occur.

Common Probability Statements: Meaning & Application

3. Common Probability Statements: Meaning & Application

If someone says the odds in favor of Justin winning the triathlon is one in ten, would you say that Justin will win for sure? Learn why this is not the case in this lesson along with other probability statements.

The Addition Rule of Probability: Definition & Examples

4. 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.

The Multiplication Rule of Probability: Definition & Examples

5. 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.

Probability of Independent and Dependent Events

6. 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.

How to Calculate Simple Conditional Probabilities

7. 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.

Applying Conditional Probability & Independence to Real Life Situations

8. 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.

Mutually Exclusive Events & Non-Mutually Exclusive Events

9. Mutually Exclusive Events & Non-Mutually Exclusive Events

In this lesson, we look at the ideas of mutually exclusive and non-mutually exclusive events. As we will learn, just because two events are non-mutually exclusive events are possible, that doesn't make them likely.

Tree Diagrams in Math: Definition & Examples

10. Tree Diagrams in Math: Definition & Examples

Explore what a tree diagram is and how to use it to organize information and answer questions about various outcomes of a particular event in this lesson. See how to create a tree diagram through multiple examples and a detailed explanation.

Probability of Simple, Compound and Complementary Events

11. 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.

Fundamental Counting Principle: Definition & Examples

12. Fundamental Counting Principle: Definition & Examples

In this lesson, you will learn about the fundamental counting principle, a method for determining how many ways choices can be made from groups. Several examples will be given.

How to Use Factorial Notation: Process and Examples

13. How to Use Factorial Notation: Process and Examples

Watch this video lesson to learn about factorial notation. Understand what it means so that you can handle it like a pro. Also see what happens when we divide factorials.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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