About This Chapter
Probability: Principles and Techniques Chapter Summary
Through these engaging text and video lessons you can review your knowledge of the principles and techniques of probability. The information covered in this chapter includes subsets of a sample space; probability of independent and dependent events; calculating simple conditional probabilities; probabilities of simple, compound, and complementary events; and the multiplication rule of probability. Once you have completed all the information in this chapter, you should feel confident in your abilities to:
- Figure simple conditional probabilities
- Discuss the relationship between conditional probabilities and independence
- Explain the addition rule of probability
- Utilize the fundamental counting principle
- Explain role of probability distributions, random numbers, and the computer in simulations
- Give examples of uniform distribution
- Know formula for binomial distribution
- List characteristics of normal distribution
Use the tools in this chapter to quickly review all the material on principles and techniques of probability, which is a convenient and flexible study guide. You can able to study on a variety of devices, on your own schedule and at your own pace so you can get through the material as quickly as you choose. Self-assessment is also possible through the quizzes following each lesson, which allows you to focus in on problem areas.
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. How to Use the Fundamental Counting Principle
There are many situations in which you will have to make several decisions simultaneously. The fundamental counting principle will help you determine how many different possible outcomes there are when you have to make multiple simultaneous decisions.
9. The Role of Probability Distributions, Random Numbers & the Computer in Simulations
Computer simulations are valuable tools used to model complex systems. In this lesson we discuss random numbers and probability distributions in relation to their role in computer simulations.
10. Uniform Distribution in Statistics: Definition & Examples
In this lesson we will explore uniform distributions and learn how to identify two basic types: discrete and uniform. You'll also learn how to recognize both by the shape and characteristics of their graphs.
11. Binomial Distribution: Definition, Formula & Examples
You have a probability distribution to create, which one do you use? That depends. In this lesson, learn about binomial distributions, get examples and criteria for their use, and learn how to calculate the binomial distribution formula.
12. Normal Distribution: Definition, Properties, Characteristics & Example
In this lesson, we will look at the Normal Distribution, more commonly known as the Bell Curve. We'll look at some of its fascinating properties and learn why it is one of the most important distributions in the study of data.
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Other chapters within the NES Mathematics Middle Grades & Early Secondary (105): Practice & Study Guide course
- Overview of Mathematical Reasoning
- Introduction to Mathematical Problem Solving
- NES Math: Properties of Real Numbers
- Understanding Relations & Functions
- Overview of Linear Functions & Equations
- Quadratic Equations, Functions & Inequalities
- Overview of Polynomial Equations, Functions & Inequalities
- Working with Absolute Values
- Overview of Rational & Radical Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- Scientific Measurement Principles & Calculations
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- Triangle Properties & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- Statistics: Principles & Techniques
- Overview of Discrete Mathematics
- Performing Operations on Matrices & Vectors
- Solving Problems with Sequences & Series
- NES Mathematics Middle Grades & Early Secondary Flashcards