Units 1 & 2 (Foundations of Probability)
Introduce foundational probability principles including sample spaces, events, and the use of Venn diagrams and tables to represent and compute probabilities. Focus on single-step and multi-step chance experiments, with attention to the concepts of independence and mutually exclusive events.

Unit 2 (Probability & Simulation Techniques)
Develop deeper understanding of conditional probability, two-way tables, and tree diagrams. Explore real-world scenarios with simulation methods to estimate probability outcomes, using random number generators and technology-based tools.

Unit 1: Foundations of Chance & Probability Theory

1.1 Introduction to Probability Concepts

• Definitions: experiment, outcome, sample space, event.

• Probability Notation: P(A), P(A∪B), P(A∩B), P(A′).

• Representing Probabilities: Venn diagrams, tables, and lists.

1.2 Calculating Basic Probabilities

• Uniform Probability Models

• Complementary Events: P(A′) = 1 − P(A)

• Mutually Exclusive Events: P(A∪B) = P(A) + P(B)

• Non-Mutually Exclusive Events: P(A∪B) = P(A) + P(B) − P(A∩B)

1.3 Multi-Step Experiments

• Tree Diagrams: for two or more steps

• Sample Space Enumeration: systematic listing

• Using Tables: to represent outcomes and compute joint probabilities

1.4 Relative Frequency & Simulation

• Experimental Probability: long-run frequency

• Simulation Techniques: using spinners, dice, coins, technology

• Random Number Generators: implementing basic simulations in technology (e.g. spreadsheets)

Unit 2: Advanced Probability Reasoning

2.1 Conditional Probability

• Definition & Notation: P(A|B), interpretation in real-world contexts

• Two-Way Tables: using frequency data to determine conditional probabilities

• Tree Diagrams with Conditional Branches

2.2 Independence vs Dependence

• Defining Independent Events: P(A∩B) = P(A)×P(B)

• Testing for Independence using conditional probability

• Real-Life Examples: exploring independence in surveys, games, etc.

2.3 Simulation of Complex Probability Models

• Using Technology: to model and estimate probabilities in large sample spaces

• Monte Carlo Simulations: basic introduction via spreadsheet or coding tools

• Critical Evaluation: comparing theoretical vs. experimental results

2.4 Application of Probability in Modelling Contexts

• Games of Chance: expected outcomes and fairness

• Risk Analysis: interpreting chance in decision-making scenarios

• Ethical Considerations: use of probability in real-life predictions and assessments