Unit 5: Probability

The Nature of Randomness: That probability describes the long-run relative frequency of an event, and that "random" does not mean "haphazard" but rather "predictable in the long run."

Fundamental Rules: The Law of Large Numbers, the Complement Rule, and the Addition and Multiplication rules.

Independence vs. Mutually Exclusive: The conceptual and mathematical difference between events that cannot happen together (disjoint) and events that do not affect each other's likelihood (independent).

Conditional Logic: How the probability of an event changes when we have "given" information that restricts the sample space.

Understand randomness, probability, and simulation

Apply probability rules in venn diagrams, two-way tables and tree diagrms

Relate conditional probability and independence

Simulation Report: Students will write a clear, step-by-step description of a simulation that accurately identifies the component, trial, and response variable.

Comparative Modeling: Given a scenario, students will correctly translate a two-way table into a Venn diagram or tree diagram to solve for specific probabilities.

Statistical Justification: Students will provide formal, formula-based arguments (DOK 3) to conclude whether two events in a real-world dataset are independent, rather than relying on intuition.