About This Chapter
The Probability Mechanics chapter of this College Algebra Help and Review course is the simplest way to master factorials and the binomial theorem. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of probability mechanics.
Who's it for?
Anyone who needs help learning or mastering college algebra material will benefit from taking this course. There is no faster or easier way to learn college-level algebra. Among those who would benefit are:
- Students who have fallen behind in understanding factorials or working with the binomial theorem.
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about probability mechanics
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How it works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Probability Mechanics chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Probability Mechanics chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any factorial or binomial theorem question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
This chapter helps students review the concepts in a Probability Mechanics unit of a standard college algebra course. Topics covered include:
- Definition of a factorial
- Evaluating factorials
- Uses of the binomial theorem in real life
- Additional applications of the binomial theorem
1. What Is a Factorial?
Maybe it's because I'm a math teacher, but when I watched the Olympics I found myself thinking about how many different ways the swimmers could have finished the race. In this video, you'll learn the answer to this question, why it's important and how it lead to the invention of the mathematical operation called the factorial.
2. Factorial Practice Problems
While the definition of factorial isn't complicated, it's easy to make them trickier by throwing a lot of them together and adding in some fractions. Test your skills here with some algebraic examples that make you use factorials without many numbers.
3. What is the Binomial Theorem?
While the F.O.I.L. method can be used to multiply any number of binomials together, doing more than three can quickly become a huge headache. Luckily, we've got the Binomial Theorem and Pascal's Triangle for that! Learn all about it in this lesson.
4. Binomial Theorem Practice Problems
The binomial theorem can be a really helpful shortcut, but it can also be really confusing. Brush up on your skills with this useful rule in these practice problems!
5. Blaise Pascal: Contributions, Inventions & Facts
Blaise Pascal contributed much to mathematics in his short 39 years. In this lesson, you will learn that he laid the foundation for probability. To help his father, Blaise even designed a calculator to make tax calculations easier.
6. Basic Probability Theory: Rules & Formulas
This lesson contains probability basics and rules, as well as the fundamental law of total probability and Bayes' theorem. Explore these important concepts and then see if you can answer the questions in the follow-up quiz.
7. Bayes' Theorem Practice Problems
Bayes' theorem is a formula used for computing conditional probability, which is the probability of something occurring with the prior knowledge that something else has occurred. In this lesson, you'll learn how to use Bayes' theorem while completing some practice problems.
8. Probability Density Function: Definition, Formula & Examples
A probability density function is a tool for building mathematical models of real-world random processes. In this lesson, we'll start by discussing why probability density functions are needed in probability theory, then we'll provide its definition and several examples of common probability density functions.
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Other chapters within the College Algebra: Help and Review course
- Basic Arithmetic
- Overview of Real Numbers
- Foundations and Linear Equations: Help and Review
- Overview of Linear Equations
- Matrices and Absolute Value: Help and Review
- Inequalities: Help and Review
- Using FOIL, Graphing Parabolas & Solving Quadratics to Factor: Help & Review
- Properties of Polynomial Functions
- Working with Quadratic Equations
- Complex Numbers: Help and Review
- Exponents and Exponential Expressions
- Overview of Exponents
- Exponents and Polynomials: Help and Review
- Algebraic Expressions and Equations
- Rational Expressions: Help and Review
- Working with Rational Expressions
- Math Expressions and Formulas
- Functions: Help and Review
- Exponentials and Logarithms: Help and Review
- Calculations, Ratios & Proportions
- Percent Notation
- Data, Statistics & Probability
- Sequences and Series: Help and Review
- Basic Number Sense and Operations
- Overview of Roots & Radical Expressions
- Overview of Continuity in Mathematics
- Overview of Mathematical Limits