# Ch 4: Probability

### About This Chapter

## Probability - Chapter Summary and Learning Objectives

Lessons in this chapter begin with an overview of basic set theory and conclude with a brief discussion on the two different approaches to probability. In between, instructors can show you the formulas and rules used to determine the likelihood of event outcomes through real-world examples and practice problems. By the end of this chapter, you should be able to do the following:

- Identify the differences between independent and dependent events
- Use addition and multiplication rules to determine the probability of events
- Explain the significance of event order in combinations and permutations

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

Mathematical Sets: Elements, Intersections & Unions | Understand basic set theory. Explain such terms as unions and intersections. |

Events as Subsets of a Sample Space: Lesson & Quiz | Define an event and identify subsets of possible experiment outcomes. |

Probability of Simple, Compound and Complementary Events | Find the probability of simple, compound and complementary events. |

Probability of Independent and Dependent Events | Determine the probability of independent and dependent events. |

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

How to Calculate Simple Conditional Probabilities | Find simple conditional probabilities using the process of dependent events. |

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

Using Two-Way Tables to Evaluate Independence: Lesson & Quiz | Evaluate independence using two-way tables. |

Applying Conditional Probability & Independence to Real Life Situations: Lesson & Quiz | Apply conditional probability to real-world scenarios. |

The Addition Rule of Probability: Definition, Examples & Quiz | Employ the addition rule of probability to calculate event outcomes. |

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

Math Combinations: Formula and Example Problems | Calculate factorials and solve combination formulas. |

How to Calculate a Permutation | Write permutations and solve for the number of possible outcomes. |

How to Calculate the Probability of Permutations | Use the permutation formula to find the probability of event outcomes in which the order of events matters. |

Relative Frequency & Classical Approaches to Probability: Lesson & Quiz | Understand the difference between relative frequency and classical approaches to probability. |

### 1. Mathematical Sets: Elements, Intersections & Unions

Mathematical sets are collections of objects or concepts that can be joined together to become mathematical building blocks. Learn about mathematical sets and understand their function in mathematics. Explore the roles of elements, intersections, and unions in mathematical sets.

### 2. Events as Subsets of a Sample Space: Definition & Example

Events can be viewed as subsets of a sample space or the result of all possible outcomes of an experiment. Learn about the definition, explanation, and real-world examples of events, subsets, and sample spaces.

### 3. Probability of Simple, Compound and Complementary Events

Probability can be calculated for simple, compound, and complementary events. Explore each type of event, understand how each event differs from the other types, and learn how to calculate each type of event's probability by reviewing examples.

### 4. Probability of Independent and Dependent Events

Probability is a ratio that predicts the likelihood an event will occur. Explore the concept of probability and understand the difference between independent and dependent events. Learn how to calculate the probability of both independent and dependent events, and review examples.

### 5. Probability of Independent Events: The 'At Least One' Rule

Independent events do not affect the outcome of events that follow, but it is generally important that they occur at least once. Learn how to use the 'At Least One' rule when calculating the probability of independent events.

### 6. How to Calculate Simple Conditional Probabilities

Conditional probability refers to the probability that an event will occur provided a previous event occurs. Learn about simple conditional probabilities and how to calculate them. Explore dependent events, understand how they differ from conditional probabilities, and review conditional probability examples.

### 7. The Relationship Between Conditional Probabilities & Independence

In everyday events, there is a clear relationship between conditional probabilities and independence. In this lesson, look at conditional and independent probabilities, how to define them, and their relationship.

### 8. Using Two-Way Tables to Evaluate Independence

In statistics, two-way tables provide a method to visualize the frequencies of two categorical variables in a data set. Learn about using two-way tables to evaluate independence in variables. Understand probability, including independent and dependent probability, and recognize how to use two-way tables to predict probability.

### 9. Applying Conditional Probability & Independence to Real Life Situations

Probability is often thought of as an inapplicable concept, but conditional probability and independence have some very real applications in everyday life. In this lesson, look at probabilities in real-life scenarios, defining conditional and independent probabilities, finding conditional and independent probabilities, and finding a given event.

### 10. The Addition Rule of Probability: Definition & Examples

The Addition Rule of Probability is a rule for finding the likelihood of two events happening at once. Explore the definition of the Addition Rule, how mutually exclusive and non-mutually exclusive events affect probability and review example problems.

### 11. The Multiplication Rule of Probability: Definition & Examples

The Multiplication Rule of Probability states that in order to find the probability of two events occurring at once, you must multiply the probability of them happening separately. Explore the definition of the Multiplication Rule of Probability, learn how to multiply independent and dependent events, and review example problems in this lesson.

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

Factorials are used to compute for a combination. Learn more about these concepts, solve the example problems in this video using the combination discussed herein, and learn an easy technique for combination problems.

### 13. How to Calculate a Permutation

A permutation is a process for placing things into a linear order. Learn how to calculate a permutation. Explore factorials and permutation notations, and review examples of permutation calculations.

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

A permutation calculates the number of outcomes where order of events matters, but not all outcomes are equally probable or favorable. Learn how to calculate the probability of permutations using functions and factorials.

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

Classical approaches to probability are approaches that use mathematics to discover the probability of certain events. Explore a classic approach to probability called relative frequency in this lesson.

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### Other Chapters

Other chapters within the Statistics 101: Principles of Statistics course