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- Learn to identify subsets
- Review methods for finding the probability of simple events
- Discover how to find the probability of independent and dependent events
- Find simple conditional probabilities
- Describe the relationship between conditional probabilities and independence
- Learn to find permutations and combinations
- Explore the multiplication rule of probability
- Learn about basic set theory.
- Understand events as subsets of a sample space.
- Calculate the probabilities of simple, compound and complementary events.
- Use the 'at least one' rule to determine the probabilities of independent events.
- Learn how to find simple conditional probabilities.
- Explain the relationship between conditional probabilities and independence.
- Use two-way tables to evaluate independence.
- Understand how to apply conditional probability and independence to real-life situations.
- Become familiar with the addition and multiplication rules of probability.
- Calculate permutations and the probability of permutations.
- Differentiate between the 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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