# Ch 4: Probability Overview

### About This Chapter

## Probability - Chapter Summary and Learning Objectives

Probability is a measure of how likely something is to occur. In this chapter, you'll learn how to calculate probabilities for different types of events and explore different rules of probability. This chapter can help you understand the following:

- Independent and dependent events
- Calculating simple conditional probabilities
- The relationship between conditional probabilities and independence
- The multiplication and addition rules of probability
- Calculating permutations

Video | Objective |
---|---|

Mathematical Sets: Elements, Intersections & Unions | Explore basic set theory |

Events as Subsets of a Sample Space: Lesson & Quiz | Learn how to identify subsets |

Probability of Simple, Compound and Complementary Events | Learn to calculate the probability of compound, simple and complementary events |

Probability of Independent and Dependent Events | Learn to calculate the probability of independent and dependent evens |

Probability of Independent Events: The 'At Least One' Rule | Use the 'at least one' rule to find the probability of independent events |

Either/Or Probability: Overlapping and Non-Overlapping Events | Use either/or probability to determine overlapping and non-overlapping events |

How to Calculate Simple Conditional Probabilities | Learn how to determine simple conditional probabilities |

The Relationship Between Conditional Probabilities & Independence: Lesson & Quiz | Look at the relationship between independence and conditional probabilities |

Using Two-Way Tables to Evaluate Independence: Lesson & Quiz | Use two-way tables to determine whether events are independent |

Applying Conditional Probability & Independence to Real Life Situations: Lesson & Quiz | Explore ways to apply conditional probability to real-life situations |

The Addition Rule of Probability: Definition, Examples & Quiz | Learn about the addition rule of probability |

The Multiplication Rule of Probability: Definition, Examples & Quiz | Learn about the multiplication rule of probability |

Math Combinations: Formula and Example Problems | Learn how to use permutations and combinations when counting |

How to Calculate the Probability of Combinations | Determine the probability of combinations |

How to Calculate a Permutation | Learn how to calculate permutations |

How to Calculate the Probability of Permutations | Determine the probability of permutations |

Relative Frequency & Classical Approaches to Probability: Lesson & Quiz | Learn about the difference between the classical approach and relative frequency |

### 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. Either/Or Probability: Overlapping and Non-Overlapping Events

Statistics is the study and interpretation of a set of data. One area of statistics is the study of probability. This lesson will describe how to determine the either/or probability of overlapping and non-overlapping events.

### 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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.

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

To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.

### 15. 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.

### 16. 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.

### 17. 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 Math 106: Contemporary Math course