Useful Links
Mathematics
Probability Theory
Probability Rules
Addition Rule
Definition
Application in events
Mutually exclusive events
Non-mutually exclusive events
Formula and Examples
\( P(A \cup B) = P(A) + P(B) - P(A \cap B) \)
Application in real-life scenarios
Multiplication Rule
Definition
Application in independent events
Independent event criteria
Example of independent events
Application in dependent events
Dependent event criteria
Calculating joint probability
Formula and Examples
\( P(A \cap B) = P(A) \times P(B|A) \)
Practical scenarios illustrating the rule
Complementary Rule
Definition
Concept of complement events
Calculation of complementary probability
Formula: \( P(A') = 1 - P(A) \)
Use cases
Simplifying calculations
Applying where outcomes are easier to count
Conditional Probability
Definition
Formula: \( P(B|A) = \frac{P(A \cap B)}{P(A)} \)
Concept of conditioning
Real-life applications
Risk analysis
Decision making in uncertainty
Conditional probability table
Bayes’ Theorem
Definition and Importance
Formula: \( P(A|B) = \frac{P(B|A)P(A)}{P(B)} \)
Components
Prior Probability
Definition and examples
Role in Bayesian framework
Likelihood
Definition and interpretation
Example scenarios
Posterior Probability
Definition and calculation
Importance in updating beliefs
Applications
Medical diagnosis
Machine learning algorithms
Fraud detection
Bayesian Decision Theory
Overview
Use in decision-making processes
Examples and case studies
3. Combinatorics and Probability
First Page
5. Random Variables