# Ch 4: Probability: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other statistics work.
- Identify the probability concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our statistics tutoring solution will benefit any student who is trying to learn about probability and earn better grades. This resource can help students including those who:

- Struggle with understanding simple, compound and complementary events; permutations and relative frequency; or any other probability topic
- Have limited time for studying
- Want a cost effective way to supplement their statistics learning
- Prefer learning statistics visually
- Find themselves failing or close to failing their probability unit
- Cope with ADD or ADHD
- Want to get ahead in statistics
- Don't have access to their statistics teacher outside of class

## Why it works:

**Engaging Tutors**: We make learning probability simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live statistics tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about probability on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Learn to identify subsets
- Review methods for finding the probability of simple events
- Discover how to find the probability of independent and dependent events
- Find simple conditional probabilities
- Describe the relationship between conditional probabilities and independence
- Learn to find permutations and combinations
- Explore the multiplication rule of probability

## Learning Objectives

- Learn about basic set theory.
- Understand events as subsets of a sample space.
- Calculate the probabilities of simple, compound and complementary events.
- Use the 'at least one' rule to determine the probabilities of independent events.
- Learn how to find simple conditional probabilities.
- Explain the relationship between conditional probabilities and independence.
- Use two-way tables to evaluate independence.
- Understand how to apply conditional probability and independence to real-life situations.
- Become familiar with the addition and multiplication rules of probability.
- Calculate permutations and the probability of permutations.
- Differentiate between the relative frequency and classical approaches to probability.

### 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.

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### Other Chapters

Other chapters within the Introduction to Statistics: Tutoring Solution course