About This Chapter
Probability - Chapter Summary and Learning Objectives
Lessons in this chapter begin with an overview of basic set theory and conclude with a brief discussion on the two different approaches to probability. In between, instructors can show you the formulas and rules used to determine the likelihood of event outcomes through real-world examples and practice problems. By the end of this chapter, you should be able to do the following:
- Identify the differences between independent and dependent events
- Use addition and multiplication rules to determine the probability of events
- Explain the significance of event order in combinations and permutations
|Mathematical Sets: Elements, Intersections & Unions||Understand basic set theory. Explain such terms as unions and intersections.|
|Events as Subsets of a Sample Space: Lesson & Quiz||Define an event and identify subsets of possible experiment outcomes.|
|Probability of Simple, Compound and Complementary Events||Find the probability of simple, compound and complementary events.|
|Probability of Independent and Dependent Events||Determine the probability of independent and dependent events.|
|Probability of Independent Events: The 'At Least One' Rule||Use the 'at least one rule' to find the probability of independent events.|
|How to Calculate Simple Conditional Probabilities||Find simple conditional probabilities using the process of dependent events.|
|The Relationship Between Conditional Probabilities & Independence: Lesson & Quiz||Understand the relationship between conditional probabilities and independence.|
|Using Two-Way Tables to Evaluate Independence: Lesson & Quiz||Evaluate independence using two-way tables.|
|Applying Conditional Probability & Independence to Real Life Situations: Lesson & Quiz||Apply conditional probability to real-world scenarios.|
|The Addition Rule of Probability: Definition, Examples & Quiz||Employ the addition rule of probability to calculate event outcomes.|
|The Multiplication Rule of Probability: Definition, Examples & Quiz||Use the multiplication rule of probability.|
|Math Combinations: Formula and Example Problems||Calculate factorials and solve combination formulas.|
|How to Calculate a Permutation||Write permutations and solve for the number of possible outcomes.|
|How to Calculate the Probability of Permutations||Use the permutation formula to find the probability of event outcomes in which the order of events matters.|
|Relative Frequency & Classical Approaches to Probability: Lesson & Quiz||Understand the difference between relative frequency and classical approaches to probability.|
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. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. Using Two-Way Tables to Evaluate Independence
If you are a visual person, a 2-way table is a great way to analyze information. This lesson shows you how to use a 2-way table to determine the independence of variables.
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 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.
14. 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.
15. Relative Frequency & Classical Approaches to Probability
To understand probability, it is important to understand the foundations. In this lesson, you will learn about relative frequency and the foundations of understanding probability.
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