# Ch 5: Discrete Probability Distributions

### About This Chapter

## Discrete Probability Distributions - Chapter Summary and Learning Objectives

Let our knowledgeable instructors introduce you to the formulas associated with discrete probability distributions and show you how they can be used to solve real-world problems. Video lessons and transcripts provide plenty of examples and practice problems to walk you through this subject matter. By the end of this chapter, you should be able to do the following:

- Find expected values using theoretical and empirical probability distributions
- Determine a binomial random variable's mean and standard deviation
- Find binomial experiment probabilities
- Use probability to evaluate game strategies

Video | Objectives |
---|---|

Random Variables: Definition, Types & Examples | Explain what a random variable is and the values or outcomes it can represent. |

Finding & Interpreting the Expected Value of a Discrete Random Variable | Show how probability distributions can be used to find expected values of a discrete random variable. |

Developing Discrete Probability Distributions Theoretically & Finding Expected Values | Demonstrate steps for developing theoretical probability distributions and finding expected values. |

Developing Discrete Probability Distributions Empirically & Finding Expected Values | Explain how to find expected values using empirical probability distributions. |

Dice: Finding Expected Values of Games of Chance | Use probability distributions to determine expected values in games involving dice. |

Cards: Finding Expected Values of Games of Chance | Learn how probability distributions can be used to determine expected values in card games. |

Lotteries: Finding Expected Values of Games of Chance | Apply probability distributions to find expected values in lotteries. |

Comparing Game Strategies Using Expected Values: Process & Examples | Find out how expected values can be used to compare game strategies. |

How to Apply Discrete Probability Concepts to Problem Solving | Use probability to solve examples of real-world problems. |

Binomial Experiments: Definition, Characteristics & Examples | Illustrate conditions of a binomial experiment. |

Finding Binomial Probabilities Using Formulas: Process & Examples | Apply the formulas used to find probabilities in an experiment with two possible outcomes. |

Practice Problems for Finding Binomial Probabilities Using Formulas | Supplement your study of binomial probabilities with practice problems and solutions. |

Finding Binomial Probabilities Using Tables | Examine binomial probability tables used to find the distribution of possible experiment outcomes. |

Mean & Standard Deviation of a Binomial Random Variable: Formula & Example | Define the mean and standard deviation and demonstrate steps for finding them. |

Solving Problems with Binomial Experiments: Steps & Example | Use binomial distributions to solve problems. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. Poker: Finding Expected Values of High Hands

In this lesson, you will learn the statistical probability of the high hands in poker, including the royal flush, straight flush, straight, and flush! This lesson will also cover the combination formula.

### 8. Poker: Finding Expected Values of Low Hands

In this lesson, you'll learn how to use the combination formula to find the probability of getting some of the lower hands in poker. You'll also test your knowledge by calculating the expected values of additional lower hands in the lesson quiz.

### 9. 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.

### 10. 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.

### 11. How to Apply Discrete Probability Concepts to Problem Solving

Discrete probability concepts, such as expected value, success, and failure, can be used to help you solve real-world problems and inform you when making decisions.

### 12. Binomial Experiments: Definition, Characteristics & Examples

Binomial experiments happen in your everyday life far more often than you might think. In this lesson, you will learn the characteristics of binomial experiments that will help you identify them.

### 13. Finding Binomial Probabilities Using Formulas: Process & Examples

You can find the probability of getting a certain number of successes when conducting a binomial experiment. In this lesson, you will learn how to find this information using the binomial probabilities formula.

### 14. Practice Problems for Finding Binomial Probabilities Using Formulas

In this lesson, you will review the binomial probability formula and the combination formula. Then follow along with the practice problems and see if you've mastered these concepts!

### 15. Finding Binomial Probabilities Using Tables

A binomial probability table can look intimidating to use. However, it can make your life a lot easier when trying to figure out binomial probabilities. This lesson will teach you how to read those tables.

### 16. Mean & Standard Deviation of a Binomial Random Variable: Formula & Example

When working with binomial random variables and experiments, it is important to understand the mean and standard deviation. In this lesson, you will learn how to analyze binomial experiments using the mean and standard deviation of a binomial random variable.

### 17. Solving Problems with Binomial Experiments: Steps & Example

Sometimes when conducting research you will need to use binomial experiments to solve problems. In this lesson, you will learn about binomial experiments and how to use probability to solve problems.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Statistics 101: Principles of Statistics course