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David Goldsman
This course provides an introduction to basic probability concepts. Our emphasis is on applications in science and engineering, with the goal of enhancing modeling and analysis skills for a variety of real-world problems.
Read more
This course provides an introduction to basic probability concepts. Our emphasis is on applications in science and engineering, with the goal of enhancing modeling and analysis skills for a variety of real-world problems.
Read more
This course provides an introduction to basic probability concepts. Our emphasis is on applications in science and engineering, with the goal of enhancing modeling and analysis skills for a variety of real-world problems.
In order to make the course completely self-contained (and to bring back long-lost memories), we’ll start off with Bootcamp lessons to review concepts from set theory and calculus. We’ll then discuss the probability axioms that serve as the basis for all of our subsequent work – what makes probability tick? That discussion will give us the tools to study elementary probability counting rules, including permutations and combinations. We’ll use these rules to work on various cool applications, including poker probability calculations and baseball line-ups!
The next venues on our tour are the concepts of independence and conditional probability, which allow us to see how the probabilities of different events are related to each other, and how new information can be used to update probabilities. The course culminates in a discussion of Bayes Rule and its various interesting consequences related to probability updates.
Register for this course and see more details by visiting:
OpenCourser.com/course/ut53q5/probability
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What's inside
Learning objectives
- Upon completion of this course, learners will be able to:
- • recall bootcamp lessons based on set theory and calculus• understand underlying probability axioms• apply elementary probability counting rules, including permutations and combinations• implement the concepts of independence and conditional probability• determine how to update probabilities via bayes rule
- Upon completion of this course, learners will be able to:
- • recall bootcamp lessons based on set theory and calculus• understand underlying probability axioms• apply elementary probability counting rules, including permutations and combinations• implement the concepts of independence and conditional probability• determine how to update probabilities via bayes rule
Syllabus
“FCPS” refers to the free text, A First Course in Probability and Statistics: free access is provided via a PDF file or as a book
Module 1: Course Introduction + Bootcamps• Lesson 1: Introduction to Probability and Statistics (FCPS §1.1)• Lesson 2 [OPTIONAL]: The Joy of Sets Bootcamp (FCPS §1.2.1)• Lesson 3 [OPTIONAL]: Calculus Bootcamp: Introduction + Derivatives (FCPS §1.2.2)• Lesson 4 [OPTIONAL]: Calculus Bootcamp: Integration and Beyond (FCPS §1.2.2)Module 2: Getting Started with Probability• Lesson 1: Experiments, Sample Spaces, and Events (FCPS §§1.3.1−1.3.2)• Lesson 2: What is Probability? (FCPS §1.3.3)• Lesson 3: Basic Probability Results (FCPS §1.3.3)• Lesson 4: Finite Sample Spaces (FCPS §1.4)• Lesson 5: Counting Techniques: Baby Examples (FCPS §1.5.1)• Lesson 6: Counting Techniques: Permutations (FCPS §1.5.2)• Lesson 7: Counting Techniques: Combinations (FCPS §1.5.3)• Lesson 8: Hypergeometric, Binomial, and Multinomial Problems (FCPS §§1.6.1−1.6.3)• Lesson 9: Permutations vs. Combinations (FCPS §1.6.4)• Lesson 10: The Birthday Problem (FCPS §1.6.5)• Lesson 11: The Envelope Problem (FCPS §1.6.6)• Lesson 12: Poker Problems (FCPS §1.6.7)• Lesson 13: Conditional Probability (FCPS §1.7.1)• Lesson 14: Independence Day (FCPS §1.7.2)• Lesson 15: Partitions and the Law of Total Probability (FCPS §1.8)• Lesson 16: Bayes Theorem (FCPS §1.8)
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Introduces basic probability concepts and applies them to real-world situations, particularly in science and engineering
Offers a comprehensive overview of probability theory, including foundational concepts, counting techniques, and advanced topics
Features expert instructors with extensive experience in probability and statistics
Covers various practical applications of probability theory, including poker probability calculations and baseball line-ups
Provides a solid foundation for further study in probability and related fields
Requires a basic understanding of set theory and calculus, which are covered in optional bootcamp lessons
Save this course
Save Probability and Statistics I: A Gentle Introduction to Probability to your list so you can find it easily later:
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Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Probability and Statistics I: A Gentle Introduction to Probability with these
activities:
Probability Notes Organization
Show steps
Enhance your understanding by organizing and summarizing the key concepts and ideas presented in the course materials.
Show steps
-
Review the course materials, including lecture notes, textbooks, and assignments.
-
Identify the most important concepts and ideas.
-
Create a concise and organized summary of the key points.
Calculus Refresher
Show steps
This activity will equip you with the essential calculus skills, making it easier for you to comprehend the probability concepts discussed in the course.
Browse courses on
Calculus
Show steps
-
Review basic calculus concepts such as derivatives and integrals.
-
Solve practice problems and review worked examples.
-
Consult online resources or textbooks for additional support.
Probability Study Group
Show steps
Engage in discussions and collaborative problem-solving sessions with peers to reinforce your understanding of probability concepts and learn from different perspectives.
Show steps
-
Form a study group with classmates or fellow learners.
-
Set regular meeting times and discuss specific probability topics.
-
Work together on practice problems and share insights.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Probability Puzzle Solving
Show steps
Engage in solving probability puzzles and problems to strengthen your analytical and problem-solving skills, enhancing your ability to apply probability concepts in real-world scenarios.
Browse courses on
Problem Solving
Show steps
-
Find online or printed collections of probability puzzles or problems.
-
Solve the puzzles or problems, carefully considering the underlying probability concepts.
-
Analyze your solutions and identify areas for improvement.
Probability Simulation with Python
Show steps
By working through Python-based tutorials, you will gain practical experience in simulating probability distributions, solidifying your understanding of the concepts.
Browse courses on
Python
Show steps
-
Find online tutorials or courses on probability simulation using Python.
-
Follow the tutorials step-by-step, implementing the code and understanding the concepts.
-
Experiment with different probability distributions and parameters.
Probability Software Exploration
Show steps
Gain practical experience by exploring and utilizing open-source software tools for probability analysis and simulation. This will enhance your ability to apply probability concepts in real-world settings.
Browse courses on
Data Analysis Tools
Show steps
-
Research and identify open-source software tools for probability analysis.
-
Install and learn how to use the chosen software.
-
Apply the software to solve practical probability problems or conduct simulations.
Probability in Practice
Show steps
Develop your understanding of how probability is used in practice by creating a presentation or report that explores applications in various fields such as data analysis, finance, or engineering.
Browse courses on
Data Analysis
Show steps
-
Choose a specific field or industry where probability is applied.
-
Research and gather data on how probability is used in that field.
-
Create a presentation or report that clearly explains the concepts and applications.
Probability Project
Show steps
Deepen your understanding and apply probability concepts by undertaking a project that involves real-world data analysis, modeling, or simulation. This will showcase your skills and provide a valuable portfolio piece.
Browse courses on
Real-World Applications
Show steps
-
Identify a problem or question that can be addressed using probability.
-
Gather relevant data and conduct exploratory analysis.
-
Develop a probability model or simulation to address the problem or question.
-
Analyze the results and draw conclusions.
Probability Notes Organization
Show steps
Enhance your understanding by organizing and summarizing the key concepts and ideas presented in the course materials.
Show steps
Show steps
Show steps
- Review the course materials, including lecture notes, textbooks, and assignments.
- Identify the most important concepts and ideas.
- Create a concise and organized summary of the key points.
Calculus Refresher
Show steps
This activity will equip you with the essential calculus skills, making it easier for you to comprehend the probability concepts discussed in the course.
Browse courses on
Calculus
Show steps
Show steps
Show steps
- Review basic calculus concepts such as derivatives and integrals.
- Solve practice problems and review worked examples.
- Consult online resources or textbooks for additional support.
Probability Study Group
Show steps
Engage in discussions and collaborative problem-solving sessions with peers to reinforce your understanding of probability concepts and learn from different perspectives.
Show steps
Show steps
Show steps
- Form a study group with classmates or fellow learners.
- Set regular meeting times and discuss specific probability topics.
- Work together on practice problems and share insights.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Probability Puzzle Solving
Show steps
Engage in solving probability puzzles and problems to strengthen your analytical and problem-solving skills, enhancing your ability to apply probability concepts in real-world scenarios.
Browse courses on
Problem Solving
Show steps
Show steps
Show steps
- Find online or printed collections of probability puzzles or problems.
- Solve the puzzles or problems, carefully considering the underlying probability concepts.
- Analyze your solutions and identify areas for improvement.
Probability Simulation with Python
Show steps
By working through Python-based tutorials, you will gain practical experience in simulating probability distributions, solidifying your understanding of the concepts.
Browse courses on
Python
Show steps
Show steps
Show steps
- Find online tutorials or courses on probability simulation using Python.
- Follow the tutorials step-by-step, implementing the code and understanding the concepts.
- Experiment with different probability distributions and parameters.
Probability Software Exploration
Show steps
Gain practical experience by exploring and utilizing open-source software tools for probability analysis and simulation. This will enhance your ability to apply probability concepts in real-world settings.
Browse courses on
Data Analysis Tools
Show steps
Show steps
Show steps
- Research and identify open-source software tools for probability analysis.
- Install and learn how to use the chosen software.
- Apply the software to solve practical probability problems or conduct simulations.
Probability in Practice
Show steps
Develop your understanding of how probability is used in practice by creating a presentation or report that explores applications in various fields such as data analysis, finance, or engineering.
Browse courses on
Data Analysis
Show steps
Show steps
Show steps
- Choose a specific field or industry where probability is applied.
- Research and gather data on how probability is used in that field.
- Create a presentation or report that clearly explains the concepts and applications.
Probability Project
Show steps
Deepen your understanding and apply probability concepts by undertaking a project that involves real-world data analysis, modeling, or simulation. This will showcase your skills and provide a valuable portfolio piece.
Browse courses on
Real-World Applications
Show steps
Show steps
Show steps
- Identify a problem or question that can be addressed using probability.
- Gather relevant data and conduct exploratory analysis.
- Develop a probability model or simulation to address the problem or question.
- Analyze the results and draw conclusions.
Career center
Learners who complete Probability and Statistics I: A Gentle Introduction to Probability will develop knowledge and skills
that may be useful to these careers:
Statistician
Statistician
Statisticians apply statistical methods to collect, analyze, interpret, and present data. This course can be a great introduction to the field of Statistics, providing a solid foundation in probability and statistical inference. The course's focus on applications in science and engineering is also valuable for Statisticians, as they often work in these fields. By taking this course, learners can gain the skills necessary to succeed in a career as a Statistician.
Data Scientist
Data Scientist
Data Scientists utilize mathematics and programming to analyze datasets and extract meaningful insights. This Probability and Statistics course can be an excellent foundation for this role, as it provides a strong understanding of probability theory and statistical concepts. These skills are essential for Data Scientists to accurately predict outcomes based on data. Additionally, the course's emphasis on real-world applications will help Data Scientists apply their knowledge to solve practical problems.
Financial Analyst
Financial Analyst
Financial Analysts use data to make informed investment decisions. This Probability and Statistics course can be very helpful for aspiring Financial Analysts, as it provides a strong foundation in probability theory and statistical methods. These skills are essential for Financial Analysts to assess risk and uncertainty, and to make sound investment decisions. By taking this course, learners can gain a competitive edge in the field of finance.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and statistical methods to improve the efficiency of organizations. This Probability and Statistics course can be very helpful for aspiring Operations Research Analysts, as it provides a strong foundation in probability theory and statistical methods. These skills are essential for Operations Research Analysts to develop and implement effective solutions to complex problems. By taking this course, learners can gain a competitive edge in the field of Operations Research.
Data Analyst
Data Analyst
Data Analysts use data to make informed decisions. This Probability and Statistics course can be a great introduction to the field of Data Analytics, providing a solid foundation in probability and statistical inference. The course's focus on applications in science and engineering is also valuable for Data Analysts, as they often work in these fields. By taking this course, learners can gain the skills necessary to succeed in a career as a Data Analyst.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical models to analyze financial data. This Probability and Statistics course can be a great foundation for aspiring Quantitative Analysts, as it provides a solid understanding of probability theory and statistical concepts. The course's emphasis on applications in science and engineering is also valuable for Quantitative Analysts, as they often work in these fields. By taking this course, learners can gain the skills necessary to succeed in a career as a Quantitative Analyst.
Actuary
Actuary
Actuaries use mathematical and statistical methods to assess risk and uncertainty in the insurance and finance industries. This Probability and Statistics course can be a great foundation for aspiring Actuaries, as it provides a solid understanding of probability theory and statistical concepts. The course's emphasis on real-world applications is also valuable for Actuaries, as they often work in these fields. By taking this course, learners can gain the skills necessary to succeed in a career as an Actuary.
Risk Analyst
Risk Analyst
Risk Analysts use data to identify and assess risk. This Probability and Statistics course can be a great foundation for aspiring Risk Analysts, as it provides a solid understanding of probability theory and statistical concepts. The course's emphasis on applications in science and engineering is also valuable for Risk Analysts, as they often work in these fields. By taking this course, learners can gain the skills necessary to succeed in a career as a Risk Analyst.
Data Engineer
Data Engineer
Data Engineers design, build, and maintain data infrastructure. This Probability and Statistics course can be helpful for aspiring Data Engineers, as it provides a solid foundation in probability and statistical methods. These skills can be useful for Data Engineers to manage and analyze large datasets. By taking this course, learners can gain a competitive edge in the field of Data Engineering.
Epidemiologist
Epidemiologist
Epidemiologists investigate the causes and patterns of disease. This Probability and Statistics course can be a great foundation for aspiring Epidemiologists, as it provides a solid understanding of probability theory and statistical concepts. The course's emphasis on applications in science and engineering is also valuable for Epidemiologists, as they often work in these fields. By taking this course, learners can gain the skills necessary to succeed in a career as an Epidemiologist.
Biostatistician
Biostatistician
Biostatisticians apply statistical methods to solve problems in biology and medicine. This Probability and Statistics course can be a great foundation for aspiring Biostatisticians, as it provides a solid understanding of probability theory and statistical concepts. The course's emphasis on applications in science and engineering is also valuable for Biostatisticians, as they often work in these fields. By taking this course, learners can gain the skills necessary to succeed in a career as a Biostatistician.
Business Analyst
Business Analyst
Business Analysts use data to improve the efficiency of organizations. This Probability and Statistics course can be helpful for aspiring Business Analysts, as it provides a solid foundation in probability and statistical methods. These skills can be useful for Business Analysts to analyze data and make recommendations for improvements. By taking this course, learners can gain a competitive edge in the field of Business Analysis.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. While not directly related to the field of Software Engineering, this Probability and Statistics course may be helpful for aspiring Software Engineers, as it provides a solid foundation in mathematical and logical thinking. These skills can be useful for Software Engineers to design and implement software systems. By taking this course, learners can gain a competitive edge in the field of Software Engineering.
Machine Learning Engineer
Machine Learning Engineer
Machine Learning Engineers design, develop, and deploy machine learning models. This Probability and Statistics course can be helpful for aspiring Machine Learning Engineers, as it provides a solid foundation in probability and statistical methods. These skills are essential for Machine Learning Engineers to develop and implement effective machine learning models. By taking this course, learners can gain a competitive edge in the field of Machine Learning Engineering.
Computer Scientist
Computer Scientist
Computer Scientists research and develop new computing technologies. While not directly related to the field of Computer Science, this Probability and Statistics course may be helpful for aspiring Computer Scientists, as it provides a solid foundation in mathematical and logical thinking. These skills can be useful for Computer Scientists to develop new algorithms and technologies. By taking this course, learners can gain a competitive edge in the field of Computer Science.
For more career information including salaries, visit:
OpenCourser.com/course/ut53q5/probability
Reading list
We've selected 14 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Probability and Statistics I: A Gentle Introduction to Probability.
Provides a more comprehensive treatment of mathematical statistics, including topics such as hypothesis testing, confidence intervals, and regression analysis. It valuable reference for students and professionals who need a deeper understanding of statistical theory and methods.
Provides a clear and concise introduction to probability theory, with a focus on applications in the social sciences. It covers topics such as probability distributions, conditional probability, and Bayesian inference.
Provides a comprehensive introduction to probability and statistics, with a focus on applications in engineering and science. It covers topics such as probability distributions, hypothesis testing, and regression analysis.
Provides a rigorous introduction to probability theory and random processes, with a focus on applications in mathematics and physics. It covers topics such as measure theory, stochastic processes, and martingales.
Provides a modern introduction to probability theory and statistics, with a focus on applications in the social sciences. It covers topics such as probability distributions, hypothesis testing, and regression analysis.
Provides a comprehensive introduction to probability and statistics, with a focus on the latest developments in statistical theory and methods. It covers topics such as Bayesian inference, machine learning, and big data.
Provides a practical introduction to machine learning, with a focus on the use of statistical methods in data analysis. It covers topics such as supervised and unsupervised learning, feature selection, and model evaluation.
Provides a practical introduction to Bayesian data analysis, with a focus on the use of statistical software. It covers topics such as Bayesian inference, model selection, and hypothesis testing.
Provides a practical introduction to Bayesian data analysis, with a focus on the use of the Stan statistical modeling language. It covers topics such as Bayesian inference, model selection, and hypothesis testing.
Provides a comprehensive introduction to mathematical statistics, with a focus on the theory of probability and its applications in statistics. It covers topics such as probability axioms, Bayesian inference, and hypothesis testing.
Provides a comprehensive introduction to probability theory, with a focus on applications in the social sciences. It covers topics such as probability distributions, hypothesis testing, and regression analysis.
Save
Provides a rigorous introduction to probability theory, with a focus on the mathematical foundations of the subject. It covers topics such as measure theory, stochastic processes, and martingales.
Save
Provides a comprehensive introduction to stochastic processes, with a focus on applications in mathematics and physics. It covers topics such as Brownian motion, Markov chains, and martingales.
Provides a comprehensive introduction to measure theory and probability theory, with a focus on the mathematical foundations of the subject. It covers topics such as Lebesgue integration, Radon-Nikodym derivatives, and conditional expectation.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/ut53q5/probability
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Probability
Effort
6 to 10 hours per week for 3 weeks
Level
Intermediate
Via
edX
Institution
The Georgia Institute of Technology
Instructor
David Goldsman
Sessions
August 17, 2026
- December 31, 2026
May 11, 2026
- August 9, 2026
January 5, 2026
- May 10, 2026
August 18, 2025
- December 31, 2025
May 12, 2025
- August 9, 2025
January 6, 2025
- May 10, 2025
August 19, 2024
- January 1, 2025
May 13, 2024
- August 11, 2024
January 8, 2024
- May 12, 2024
Language
English
Transcript
English
This course belongs to a
collection
called
Probability/Random Variables. It's comprised of two courses:
- Probability and Statistics I: A Gentle Introduction to Probability (viewing)
- Probability and Statistics II: Random Variables – Great Expectations to Bell Curves
Good to know
Introduces basic probability concepts and applies them to real-world situations, particularly in science and engineering
Offers a comprehensive overview of probability theory, including foundational concepts, counting techniques, and advanced topics
Features expert instructors with extensive experience in probability and statistics
Covers various practical applications of probability theory, including poker probability calculations and baseball line-ups
Provides a solid foundation for further study in probability and related fields
Requires a basic understanding of set theory and calculus, which are covered in optional bootcamp lessons
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