1. What is Probability?

2. Basic Terminology

   1. Experiment, Outcome, Event, Sample Space

   2. Random vs Deterministic Experiments

3. Types of Probability

   1. Theoretical (Classical) Probability

   2. Experimental (Empirical) Probability

   3. Subjective Probability

Counting Principles (For Probability) 

1. Fundamental Principle of Counting

2. Permutations

   1. Without Repetition

   2. With Repetition

3. Combinations

   1. Without Repetition

   2. With Repetition

4. Applications of Counting in Probability

Random Variables and Probability Distributions 

1. Discrete and Continuous Random Variables

2. Probability Mass Function (PMF)

3. Probability Density Function (PDF)

4. Cumulative Distribution Function (CDF)

5. Expected Value (Mean) of a Random Variable

6. Variance and Standard Deviation

7. Bernoulli Trials

Continuous Probability Distributions 

1. Uniform Distribution (Continuous)

2. Normal Distribution
   Standard Normal Distribution (Z-distribution)

   1. Using Z-tables

3. Exponential Distribution

4. Gamma Distribution (Advanced)

5. Beta Distribution (Advanced)

Limit Theorems and Advanced Concepts 

1. Probability of an Event

2. Complement of an Event

3. Addition Rule

   1. For Mutually Exclusive Events

   2. For Non-Mutually Exclusive Events

4. Multiplication Rule

   1. Independent Events

   2. Dependent Events

5. Conditional Probability

6. Law of Total Probability

7. Bayes’ Theorem

Set Theory and Probability 

1. Sets and Subsets

2. Venn Diagrams

3. Union, Intersection, and Complement of Events

4. Using Venn Diagrams to Solve Probability Problems

Discrete Probability Distributions 

1. Uniform Distribution (Discrete)

2. Binomial Distribution

3. Geometric Distribution

4. Negative Binomial Distribution

5. Hypergeometric Distribution

6. Poisson Distribution

Joint, Marginal, and Conditional Distributions 

1. Joint Probability Distributions

2. Marginal Probability

3. Conditional Probability (again, in multivariate context)

4. Independence of Random Variables

5. Covariance and Correlation

Bayesian Probability (Advanced) 

1. Prior and Posterior Probability

2. Likelihood Function

3. Bayes' Theorem in Statistical Inference

4. Bayesian vs Frequentist Approaches

Applications of Probability