Practice

Take a guided, problem-solving based approach to learning Probability. These compilations provide unique perspectives and applications you won't find anywhere else.

Introduction to Probability

What's inside

• Understanding Probability
• Computing Probabilities
• Assumptions and Models

Perplexing Probability

What's inside

• Introduction
• Brain-Warping Probability
• Crazy Mad Dice

Casino Probability

What's inside

• Introduction
• Blackjack
• Casino Craps
• Poker

Community Wiki

Browse through thousands of Probability wikis written by our community of experts.

Counting

• Rule of Sum
• Counting Integers in a Range
• Rule of Product
• Rule of Sum and Rule of Product Problem Solving
• Counting Shapes
• Discrete Mathematics
• Set Complement
• Permutations
• Permutations with Repetition
• Permutations With Restriction
• Combinatorics
• Combinations
• Rectangular Grid Walk

Sets and Partitions

• Set Theory
• Set
• Sets - Elements
• Sets - Subsets
• Classical Sets
• Cardinality
• Partially Ordered Sets
• ZFC
• Ordinal Numbers
• Venn Diagram
• Union and Intersection
• Principle of Inclusion and Exclusion (PIE)
• Double Counting
• Derangements
• Bijection, Injection, And Surjection
• Bijective Functions
• Burnside's Lemma
• Pigeonhole Principle
• Ramsey Theory
• Dilworth's Theorem
• Distinct Objects into Distinct Bins
• Distinct Objects into Identical Bins
• Identical Objects into Distinct Bins
• Identical Objects into Identical Bins
• Partition of an Integer

Data

• Mean (Average)
• Interquartile Range (IQR)
• Understanding Data - Problem Solving
• Data Presentation - Tables
• Data Presentation - Bar Charts
• Data Presentation - Pie Charts
• Data Presentation - Dot Diagram
• Data Presentation - Histogram
• Data Presentation - Stem-leaf plot

Probability

• Probability
• Uniform Probability (by Outcomes)
• Probability - Rule of Sum
• Probability - Rule of Product
• Probability - By Complement
• Probability - Problem Solving
• Math of Poker - Basics
• Conditional Probability
• Probability - Independent events
• Probabilistic Principle of Inclusion and Exclusion
• Bayes' Theorem and Conditional Probability
• Conditional Probability Distribution
• Monty Hall Problem
• Bayesian Theory in Science and Math
• Poker Strategy
• Expected Value
• Linearity of Expectation
• Law of Iterated Expectation
• Coupon Collector Problem
• Variance
• Standard Deviation
• Covariance
• Geometric Probability

Random Variables

• Discrete Random Variables - Definition
• Discrete Random Variables - Probability Density Function (PDF)
• Discrete Random Variables - Cumulative Distribution Function
• Discrete Random Variables - Joint Probability Distribution
• Discrete Random Variables - Indicator Variables
• Continuous Random Variables - Definition
• Continuous Random Variables - Probability Density Function (PDF)
• Continuous Random Variables - Cumulative Distribution Function
• Continuous Random Variables - Joint Probability Distribution
• Bernoulli Distribution
• Binomial Distribution
• Geometric Distribution
• Poisson Distribution
• Hypergeometric Distribution
• Continuous Probability Distributions - Uniform Distribution
• Normal Distribution
• Exponential Distribution
• Log-normal Distribution
• Multivariate Normal Distribution
• Statistics
• Sampling (Statistics)
• Chi-Squared Test
• Maximum Likelihood Estimation (MLE)
• Inverse Transform Sampling
• Statistical Significance
• Markov Chains
• Stationary Distributions of Markov Chains
• Transience and Recurrence of Markov Chains
• Ergodic Markov Chains
• Absorbing Markov Chains

Binomial Theorem

• Binomial Coefficient
• Pascal's Triangle
• Binomial Theorem
• Negative Binomial Theorem
• Fractional Binomial Theorem
• Multinomial Coefficients
• Multinomial Theorem

Recurrence Relations

• Recursion
• Recurrence Relations
• Fractals
• Minkowski Dimension
• Fibonacci Sequence
• Linear Recurrence Relations

Advanced Discrete

• Combinatorial Games - Definition
• Combinatorial Games - Winning Positions
• Sprague Grundy Theorem
• Nim
• Dots and Boxes
• Fair Division
• Axiom of Determinacy
• Casework
• Conjectures
• Construction
• Extremal Principle
• Invariant Principle
• Vandermonde's Identity
• Hockey Stick Identity
• Graph Theory
• Eulerian Path
• Hamiltonian Path
• Four Color Theorem
• Graph Coloring and Chromatic Numbers
• Hall's Marriage Theorem
• Applications of Hall's Marriage Theorem
• Art Gallery Problem
• Wiki Collaboration Graph
• Combinatorial Optimization
• Group actions
• Generating Functions
• Manipulating Generating Functions
• Coloring (Parity Arguments)
• Knots