About This Chapter
Chance & Probability - Chapter Summary
This chapter was made to test your knowledge and skills related to probability. Complete them to study the different ways of representing probability, the different types of probability and the calculations used to determine them. The key topics covered in this chapter include:
- Elements, intersections and unions of mathematical sets
- Showing events as subsets of a sample space
- Rules and formulas of basic probability
- Probability for simple and compound events
- How to find the probability of independent and dependent events
- Calculations for simple conditional probability
- Finding the probability of permutations
- Classic approaches to probability and relative frequency
Complete several lesson quizzes as a way of evaluating your comprehension. When all of the lessons have been explored, you may also take the practice chapter exam to ensure that you thoroughly understand chance and 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. 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.
4. 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.
5. 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.
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. 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.
8. 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.
9. Probability of Compound Events: Definition & Examples
Determining the probability of compound events involves finding the probability of each event and then determining how to combine them. This lesson will give you the tools to find the probability and finish with a quiz to cement your knowledge.
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