- Basic Probability Concepts
- Key Definitions
- Different Approaches to Probability
- Event Operations
- Sample Spaces with Equally Likely Outcomes
Sample Space
Events
- Observation
- Statistical Experiment
- Sample Space (A set)
- Sample Point/ Outcome
- Event (Also a Set)
- Sure Event
- Null Event
- Simple Event
- Compound Event
- Union (Logical OR)
- Intersection (Logical AND)
- Complement (Logical NOT)
- Mutually Exclusive
- Subset
- Equal Set
- De Morgan's Law
- The 3 Rules for Events (Set Theory)
- Counting Tools
- Generalized Basic Principle of Counting (GBPC)
- Addition Rule
- Factorials (Specialization of GBPC)
- Permutation (Specialization of Factorials)
- Combinations
- P & C (Using both P & C, with Addition Rule)
- Need to know special cases for Permutations
- Need to know special cases for Combinations
- Equally Likely Outcomes
- Frequency Based
- Personal / Subjective
- Axioms of Probability
- 0 <= P(A) <= 1
- P(S) = 1
- Union of all mutually exclusive events in S = Sum of numerical probabilities of each of those events
- Properties of Probability
- Complements of an Event
- Null Event
- Probability of finite sequence of mutually exclusive events
- Bigger Set, Bigger Probability
- Inclusion Exclusion Principle for N Events
P(A) = |A| / |S|
- Computing Probabilities
- Use P&C
- Use Set Theory
- Use Properties / Axioms of Probability
- Famous Examples: Birthday Problem and Inverse Birthday problem
- Conditional Probabilities
- Independent Events
- Bayes Theorem
- Definition of Conditional Probability
- Mental Model of Reduced Sample Spaces
- Using Axioms and Properties of Probability on Conditional Probability of (.|A), as long as given condition is constant
- Generalized Multiplication Rule and Probability Trees
- Inverting Conditional Probability
- Definition of Independent Events and its implication