About This Chapter
Binomial Theorem & Probability - Chapter Summary
This informative chapter covers binomial theorem and probability, including the definition of the binomial theorem and how it's used to expand a binomial. Our helpful lessons clearly explain the relationship between Pascal's Triangle and combinations, as well as give examples of finite sequences. You'll also review the formula used for binomial distribution, as well as examples of this concept. This chapter is designed to help you:
- Use Pascal's Triangle with polynomials
- Explain what a finite series is
- Calculate binomial probability using a formula
Our lessons and quizzes make studying even the most challenging topics simple and fun. Access these learning tools on your mobile phone, tablet or computer 24 hours a day to study at whatever time works best for you. If you need assistance, contact one of our instructors for help as you work through the chapter.
1. 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.
2. Pascal's Triangle: Definition and Use with Polynomials
Pascal's Triangle is defined and discussed briefly. Following the introduction to the triangle, its use in expanding polynomial powers is elaborated with examples.
3. How to Use the Binomial Theorem to Expand a Binomial
In this video lesson, you will see what the binomial theorem has in common with Pascal's triangle. Learn how you can use Pascal's triangle to help you to easily expand a binomial.
4. The Relationship Between Pascal's Triangle & Combinations
Pascal's triangle shows many important mathematical concepts like the counting numbers and the binomial coefficients. In this lesson, we show how Pascal's triangle is related to combinations.
5. Finite Sequence: Definition & Examples
After completing this lesson, you will be able to identify a finite sequence and different types of finite sequences. You will also be able to distinguish mathematical patterns of finite sequences.
6. What is a Finite Series?
Read this lesson to learn how finite series are necessary for things such as the Binomial Theorem. You'll also learn how some other mathematical concepts can only be performed with finite series.
7. Calculating Binomial Probability: Formula & Examples
When we're calculating probabilities and there are only two possible outcomes, we can consider using the binomial probability. In this lesson we'll look at the conditions for using this probability, the formula, and some examples that clarify how to use it.
8. 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.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards