# Ch 6: Probability Combinations, Permutations & Expected Values

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### About This Chapter

## Probability Combinations, Permutations & Expected Values - Chapter Summary and Learning Objectives

Explore the formulas and calculations associated with math combinations and permutations in this chapter and then watch as games of chance, like poker and blackjack, are used to show you how to find expected values. Each lesson takes a larger concept, like permutations, and breaks it down into small chunks of topics that are easier to learn and retain. Before you progress to the next lesson, make sure you understand the concepts presented in the current video by taking the self-assessment quiz that follows it. As you make your way through these lessons, you'll learn about:

- Methods for calculating permutations and probabilities of permutations
- Classical approaches to probability
- Types of random variables
- Discrete probability distributions
- Game strategies that use expected values

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

Math Combinations: Formula and Example Problems | Learn the formulas used for math combinations and check out examples that walk you through the process of using them. |

How to Calculate a Permutation | Study the steps you'll use to calculate permutations. |

How to Calculate the Probability of Permutations | Determine the best way to calculate the probability of permutations. |

Relative Frequency & Classical Approaches to Probability: Lesson & Quiz | Explore these different approaches to probability. |

Finding & Interpreting the Expected Value of a Discrete Random Variable | Discover how to use probability distributions to find expected values. |

Random Variables: Definition, Types & Examples | Identify various types of random variables. |

Developing Discrete Probability Distributions Theoretically & Finding Expected Values | Get a firsthand look at the process of theoretically developing discrete probability distributions. |

Developing Discrete Probability Distributions Empirically & Finding Expected Values | Examine the ways that you can empirically develop a discrete probability distribution. |

Dice: Finding Expected Values of Games of Chance | Differentiate between dependent and independent probability events using dice. |

Blackjack: Finding Expected Values of Games of Chance with Cards | Determine how to calculate expected values of betting games and probabilities of certain hands. |

Poker: Finding Expected Values of Games of Chance with Cards | Learn to calculate probabilities of games of chance using poker. |

Lotteries: Finding Expected Values of Games of Chance | Calculate expected values of lottery games. |

Comparing Game Strategies Using Expected Values: Process & Examples | Understand how to use expected values to determine the strength of different game strategies. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. Finding & Interpreting the Expected Value of a Discrete Random Variable

Discrete random variables appear in your life a lot more than you think. You can use expected values to find the probability of a discrete random variable, as shown in this lesson.

### 6. Random Variables: Definition, Types & Examples

This lesson defines the term random variables in the context of probability. You'll learn about certain properties of random variables and the different types of random variables.

### 7. Developing Discrete Probability Distributions Theoretically & Finding Expected Values

In this lesson, we will look at generating a theoretical probability distribution for a discrete random variable and introduce the concept of expected value.

### 8. Developing Discrete Probability Distributions Empirically & Finding Expected Values

In this lesson, we will look at creating a discrete probability distribution given a set of discrete data. We will also look at determining the expected value of the distribution.

### 9. Dice: Finding Expected Values of Games of Chance

This lesson examines the various combinations and probabilities behind rolling dice. We will look at a game of dice and what to expect to win or lose in a game. In addition we will extend these concepts to playing with different sided dice.

### 10. Blackjack: Finding Expected Values of Games of Chance with Cards

In this video we learn about games of cards, and how to calculate probabilities. We look at the game of Blackjack and calculate the probability of getting certain hands. In addition we demonstrate how to calculate the expected value of a game that involves betting.

### 11. Lotteries: Finding Expected Values of Games of Chance

Most of us won't have a problem with winning the lottery. But is it a realistic goal? Do you really have a chance? In this lesson, learn how luck and probability collide when finding expected values in games of chance.

### 12. Comparing Game Strategies Using Expected Values: Process & Examples

While statistics and probability leave a lot to chance, we can use expected values to help inform our decisions. This lesson shows us how to use expected values to make the best determinations possible.

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### Other Chapters

Other chapters within the DSST Principles of Statistics: Study Guide & Test Prep course

- Data Types & Measurements in Statistics
- Sampling Methods in Statistics
- Descriptive Statistics of Data Sets
- Visual Representations in Statistics
- Probability: Rules for Events
- Probability: Discrete & Continuous Distributions
- Correlation & Regression in Statistics
- Sampling Distributions in Statistics
- Hypothesis Testing in Inferential Statistics