About This Chapter
Honors Algebra 1: Probability & Statistics - Chapter Summary and Learning Objectives
The lessons in this chapter will teach you about probability and statistics. Each is a short video with a quiz to be taken at the end to test your understanding of the material. If you need to review something, either use the video transcript or use the video timeline tool to replay the exact section you want. You can ask a question of the instructor, and you can monitor your progress on your dashboard. When you complete this chapter, you should have a better understanding of:
- Mathematical sets
- Conditional and either/or probability
- Overlapping and non-overlapping events, independent and dependent events
- The relationship between conditional probabilities and independence
- The addition and multiplication rules of probability
- Combinations and permutations in probability
|Mathematical Sets: Elements, Intersections & Unions||Explore the intersections and unions of mathematical sets.|
|Events as Subsets of a Sample Space: Definition & Example||Analyze the concept of events as subsets.|
|Conditional Probability: Definition & Uses||Learn about conditional probability.|
|How to Calculate Simple Conditional Probabilities||See how to calculate how a previous event will affect the current event.|
|Either/Or Probability: Overlapping and Non-Overlapping Events||Compare the either/or/probability of overlapping and non-overlapping events.|
|Probability of Independent and Dependent Events||Differentiate between the probability of independent and dependent events.|
|Probability of Independent Events: The 'At Least One' Rule||Examine the 'At Least One' rule.|
|The Relationship between Conditional Probabilities & Independence||Look at the similarities and differences between conditional probabilities and independence.|
|Applying Conditional Probability & Independence to Real Life Situations||Get familiar with conditional probability and independence in real life situations.|
|The Addition Rule of Probability: Definition & Examples||Apply the addition rule of probability.|
|The Multiplication Rule of Probability: Definition and Examples||Learn to use the multiplication rule of probability.|
|Math Combinations: Formula and Example Problems||Get familiar with math combinations and permutations.|
|How to Calculate the Probability of Combinations||Consider how to calculate the probability of combinations.|
|How to Calculate a Permutation||Examine the calculation of a permutation.|
|How to Calculate the Probability of Permutations||Work out how to find the probability of a permutation.|
1. Mathematical Sets: Elements, Intersections & Unions
Today we're going to explore mathematical sets, which are surprisingly simple! Sets are just collections of any objects or concepts, also known as elements, that can be related to each other through union or intersection.
2. 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.
3. Conditional Probability: Definition & Uses
We know a coin can land on either heads or tails. But what would happen if one coin flip changed the next? In this lesson, we'll look at events that are dependent on each other, and we'll learn how to calculate the probability of two events occurring in a combined manner.
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. Either/Or Probability: Overlapping and Non-Overlapping Events
Statistics is the study and interpretation of a set of data. One area of statistics is the study of probability. This lesson will describe how to determine the either/or probability of overlapping and non-overlapping events.
6. 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.
7. Probability of Independent Events: The 'At Least One' Rule
Occasionally when calculating independent events, it is only important that the event happens once. This is referred to as the 'At Least One' Rule. To calculate this type of problem, we will use the process of complementary events to find the probability of our event occurring at least once.
8. 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.
9. Applying Conditional Probability & Independence to Real Life Situations
It can be really confusing learning how to apply conditional and independent probability to real-life situations. This lesson focuses on several examples and practice problems to help you learn how to find conditional probability.
10. 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.
11. 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.
12. 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.
13. How to Calculate the Probability of Combinations
To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.
14. 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.
15. 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.
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Other chapters within the Honors Algebra 1 Textbook course
- Honors Algebra 1: Basic Arithmetic Review
- Honors Algebra 1: Fractions & Decimal Review
- Honors Algebra 1: Calculations, Ratios, Percent & Proportions
- Honors Algebra 1: Properties of Real Numbers
- Honors Algebra 1: Exponents & Scientific Notation
- High School Algebra: Radical Expressions
- Honors Algebra 1: Composing Algebraic Equations & Expressions
- Honors Algebra 1: Solving Algebraic Expressions & Equations
- Honors Algebra 1: Properties of Functions
- Honors Algebra 1: Absolute Value Expressions & Equations
- Honors Algebra 1: Matrices in Linear Equations
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Properties of Polynomial Functions
- Honors Algebra 1: Vectors in Linear Algebra
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- Honors Algebra 1: Linear Equations
- High School Algebra: Factoring
- Honors Algebra 1: Factoring with FOIL, Graphing Parabolas & Solving Quadratics
- Honors Algebra 1: Graphing & Factoring Quadratic Equations
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- Honors Algebra 1: Descriptive Statistics
- Honors Algebra 1: Data Analysis
- Honors Algebra 1: Units of Measurement in Geometry
- Honors Algebra 1: Shapes of Geometry
- Honors Algebra 1: Similar Polygons
- Honors Algebra 1: Pre-Calculus Geometry
- High School Algebra: Well-Known Equations
- Honors Algebra 1: Maximum & Minimum Value of Functions
- Honors Algebra 1: Patterns in Math