Build a solid foundation in probability theory and counting
All possible outcomes
Likelihood of an event
Given that B occurred
Update beliefs with evidence
Probability is the mathematics of uncertainty. From weather forecasts to medical diagnoses, probability helps us make informed decisions in an uncertain world. Start your journey by understanding the fundamental concepts that underpin all of probability theory.
Master the fundamentals of probability theory
All sections are accessible - follow the numbered sequence for the best learning experience
Overall Progress
0%
Build formulas step-by-step
Master the fundamental formulas of probability by building them interactively. Click on each part to understand why it's there and how it works.
Key topics:
Physical intuition for probability
Build intuitive understanding of probability through physical models. Learn the physical foundations before the mathematical notation.
Key topics:
The probability language bridge
Master the translation between everyday English and mathematical notation. Your essential reference for converting word problems to math.
Key topics:
Events, sets, and the grammar of probability
Master sample spaces, events, and set operations in one unified approach. Learn Venn diagrams, De Morgan's laws, and how to build complex events.
Key topics:
Fundamental counting principle
Learn systematic counting methods for multi-stage procedures. Master the multiplication principle for complex scenarios.
Key topics:
Permutations and arrangements
Understand when order matters. Calculate permutations with and without replacement using factorial notation.
Key topics:
Combinations and selections
Master combinations when order doesn't matter. Calculate binomial coefficients and explore Pascal's triangle.
Key topics:
Classical probability definition
Apply the classical definition of probability. Master the addition rule and calculate probabilities from counting.
Key topics:
Probability given information
Master conditional probability and independence. Apply the multiplication rule and Law of Total Probability.
Key topics:
Updating beliefs with evidence
Learn to update probabilities with new evidence. Apply Bayes' theorem to real-world problems like medical testing.
Key topics:
Common probability mistakes
Identify and avoid common probability errors. Understand the gambler's fallacy, base rate neglect, and more.
Key topics:
The famous probability paradox
Explore the counterintuitive Monty Hall problem through interactive simulations. See why switching doors doubles your chances of winning!
Key topics:
Start with fundamentals to understand the core concepts
Apply concepts to real-world data to reinforce understanding
Learn when and how to apply each concept effectively