# Ch 4: Probability: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering college statistics material will benefit from taking this course. There is no faster or easier way to learn college statistics. Among those who would benefit are:

- Students who have fallen behind in understanding mathematical sets or working with events as subsets of a sample space
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about probability
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Probability chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know; review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Probability chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any probability question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

This chapter helps students review the concepts in a Probability unit of a standard college-level principles of statistics course. Topics covered include:

- Probability of simple, compound and complementary events
- How to calculate simple conditional probabilities
- Using two-way tables to evaluate independence
- The addition and multiplication rules of probability
- How to calculate a permutation

### 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.

### 12. Math Combinations: Formula and Example Problems

Combinations are an arrangement of objects where order does not matter. In this lesson, the coach of the Wildcats basketball team uses combinations to help his team prepare for the upcoming season.

### 13. How to Calculate a Permutation

A permutation is a method used to calculate the total outcomes of a situation where order is important. In this lesson, John will use permutations to help him organize the cards in his poker hand and order a pizza.

### 14. How to Calculate the Probability of Permutations

In this lesson, you will learn how to calculate the probability of a permutation by analyzing a real-world example in which the order of the events does matter. We'll also review what a factorial is. We will then go over some examples for practice.

### 15. Relative Frequency & Classical Approaches to Probability

To understand probability, it is important to understand the foundations. In this lesson, you will learn about relative frequency and the foundations of understanding probability.

### 16. What is Theoretical Probability? - Definition, Formula & Examples

Have you ever heard someone ask, 'What are the odds?' Usually what it is meant is, 'How likely is it that an event will happen?' This lesson explores finding the likelihood, or theoretical probability, that an event could occur.

### 17. Comparing Theoretical & Experimental Probability

Did you know there's more than one kind of probability? Complete this lesson to compare theoretical probability with experimental probability. They're not the same!

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### Other Chapters

Other chapters within the Introduction to Statistics: Help and Review course

- Overview of Statistics: Help and Review
- Summarizing Data: Help and Review
- Tables and Plots: Help and Review
- Discrete Probability Distributions: Help and Review
- Continuous Probability Distributions: Help and Review
- Sampling: Help and Review
- Regression & Correlation: Help and Review
- Hypothesis Testing in Statistics