Master the Building Blocks of Probability: Learn Fundamentals, Theories, and Practical Applications.

What you will learn

### Understand the basic concepts of probability including sample spaces, events, and axioms of probability.

### Be able to calculate the probabilities of events using permutations, combinations, and conditional probability.

### Understand discrete and continuous random variables and their associated probability distributions .

### Be able to calculate expected values, variances, and standard deviations of both discrete and continuous random variables.

Description

Introduction to Probability is an introductory course that provides an overview of probability theory and its applications. The course covers various topics related to probability including sample spaces and events, permutations and combinations, axioms of probability, conditional probability and independence, Bayes theorem, discrete random variables, and continuous random variables.

The course starts with an introduction to sample spaces and events, which are the basic building blocks of probability theory. Students will learn how to use these concepts to analyze and solve probability problems. The next topic covered is permutations and combinations, which are used to calculate the number of possible outcomes in a given situation, then we move on to the axioms of probability, which provide the theoretical underpinnings of probability theory. Students will learn about the three axioms of probability and how these principles can be used to solve probability problems.

Next, we use all of these fundamentals to solve a popular probability problem known as the birthday problem. Students will learn how to calculate the probability of two people sharing the same birthday in a group of people.

Conditional probability and independence are also introduced in the course. Students will learn how to calculate the probability of an event given that another event has occurred. Bayes theorem is covered in the course, which is a powerful tool in probability theory. Students will learn how to use this theorem to calculate probabilities when given additional information. After learning about conditional probability and Bayes theorem we will move on to understand discrete random variables and continuous random variables.

In conclusion, this course provides students with a comprehensive introduction to probability theory and its applications. It covers a wide range of topics and provides students with the tools they need to solve a variety of probability problems. By the end of the course, students will have a solid foundation in probability theory and will be able to apply these principles to real-world situations.

Content

### Probability, Counting, and Axioms

### Conditional Probability

### Discrete Random Variables

### Continuous Random Variables