Lesson 1: 14.1 Counting Principles

How can we systematically count all the possible outcomes of a multi-step event?
What is the relationship between the number of choices at each step and the total number of outcomes?
How can we use multiplication to efficiently calculate the total number of possibilities?

Fundamental Counting Principle
Event
Outcome
Sample Space
Independent Events
Dependent Events

HS.MA.5A - 5A. Summarize, represent, and interpret data on a single count or measurement variable.

Systematically counting outcomes: Counting principles provide a structured approach to count all possible outcomes of an event, ensuring that no outcome is missed.
Calculating probabilities: By knowing the total number of outcomes, we can calculate the probability of specific events occurring.
Making informed decisions: Counting principles help us assess the potential consequences of different choices and make informed decisions.
Understanding complex systems: Counting principles can be used to analyze complex systems with many variables and interactions.
DOK Levels 1-3

Example 7, page 880: A multiple-choice test has five questions with four choices for each question. In how many different ways can the test be completed?

Knowing when repetition is allowed and when it is not.

For advanced students, introduce more complex problems involving multiple stages or conditional probabilities.
For struggling students, provide additional examples and visual aids.

Exit tickets and quizzes

Textbook in class

Notes posted on Google Classroom