Introduction to Basic Probability Concepts

Offered by GTx

Course Description

"Introduction to Basic Probability Concepts" is an engaging and comprehensive course offered by GTx, designed to equip students with fundamental probability skills essential for science and engineering applications. This intermediate-level course delves into the fascinating world of probability theory, providing learners with a solid foundation to enhance their modeling and analysis capabilities for real-world problems.

What Students Will Learn

  • Apply probability axioms to solve complex problems
  • Utilize elementary probability counting rules, including permutations and combinations
  • Analyze independence and conditional probability in various scenarios
  • Implement Bayes Rule to update probabilities based on new information
  • Develop critical thinking skills for probability modeling in real-world applications

Pre-requisites

  • Basic knowledge of set theory
  • Fundamental understanding of calculus
  • Some experience with computer programming (e.g., Excel)

Note: The course provides bootcamp lessons to refresh your memory on these topics.

Course Content

  • Set theory and calculus review
  • Probability axioms and their applications
  • Elementary probability counting rules
  • Permutations and combinations
  • Hypergeometric, binomial, and multinomial problems
  • Conditional probability and independence
  • Law of Total Probability
  • Bayes Theorem and its consequences

Who This Course Is For

  • Science and engineering students looking to enhance their probability skills
  • Professionals seeking to improve their data analysis and decision-making abilities
  • Anyone interested in gaining a deeper understanding of probability theory and its real-world applications

Real-World Applications

  • Improving risk assessment in engineering projects
  • Enhancing decision-making processes in business and finance
  • Developing more accurate predictive models in data science
  • Solving complex problems in scientific research
  • Optimizing strategies in fields such as healthcare, logistics, and manufacturing

Syllabus

Module 1: Course Introduction + Bootcamps

  • Introduction to Probability and Statistics
  • The Joy of Sets Bootcamp (Optional)
  • Calculus Bootcamp: Introduction + Derivatives (Optional)
  • Calculus Bootcamp: Integration and Beyond (Optional)

Module 2: Getting Started with Probability

  • Experiments, Sample Spaces, and Events
  • What is Probability?
  • Basic Probability Results
  • Finite Sample Spaces
  • Counting Techniques: Baby Examples
  • Counting Techniques: Permutations
  • Counting Techniques: Combinations
  • Hypergeometric, Binomial, and Multinomial Problems
  • Permutations vs. Combinations
  • The Birthday Problem
  • The Envelope Problem
  • Poker Problems
  • Conditional Probability
  • Independence Day
  • Partitions and the Law of Total Probability
  • Bayes Theorem