Classroom Resource

Count Outcomes Using Tree Diagram

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

Tree diagrams display all the possible outcomes of an event. Each branch in a tree diagram represents a possible outcome. Tree diagrams can be used to find the number of possible outcomes and calculate the probability of possible outcomes.

Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.39

Compute the conditional probability of event A given event B, using two-way tables or tree diagrams.

Unpacked Content

UP:MA19.A1.39

Vocabulary

  • Conditional probability
  • Independence
  • Probability

Knowledge

Students know:
  • Methods to find probability using two-way tables or tree diagrams.
  • Techniques to find conditional probability.

Skills

Students are able to:
  • Accurately determine the probability of events from a two-way table or tree diagram.

Understanding

Students understand that:
  • The independence of two events is determined by the effect that one event has on the outcome of another event.
  • The occurrence of one event may or may not influence the likelihood that another event occurs.
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.6

Use multiple representations and methods for counting objects and developing more efficient counting techniques. Note: Representations and methods may include tree diagrams, lists, manipulatives, overcounting methods, recursive patterns, and explicit formulas.

Unpacked Content

UP:MA19.FM.6

Vocabulary

  • Tree diagram
  • Recursive pattern
  • Explicit formula

Knowledge

Students know:

  • Tree diagrams can be used to systematically list all possibilities for a given set of constraints.

Skills

Students are able to:

  • List all possible outcomes for a given set of constraints

Understanding

Students understand that:

  • Tree diagrams and other systematic methods can be used to count objects but may not be the most efficient method when counting large quantities.
  • Recursive and explicit formulas can be developed from examining patterns in tree diagrams and systematic lists.

Body

  1. Use multiple representations and methods for counting objects and developing more efficient counting techniques. Note: Representations and methods may include tree diagrams, lists, manipulatives, overcounting methods, recursive patterns, and explicit formulas.
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.7

Develop and use the Fundamental Counting Principle for counting independent and dependent events.

Unpacked Content

UP:MA19.FM.7

Vocabulary

  • Fundamental counting principle
  • Independent events
  • Dependent events
  • Tree diagram
  • Branches
  • Node

Knowledge

Students know:

  • How to construct a tree diagram.

Skills

Students are able to:

  • Count the number of events when given a variety of constraints/parameters when the Fundamental Counting Principle can be applied.

Understanding

Students understand that:

  • The Fundamental Counting Principle can be applied in contexts where an ordered list of events occur and there are a ways for the first event to occur, b ways for the second event to occur so the number of ways of the ordered sequence of events occuring is axb.

Body

  1. Develop and use the Fundamental Counting Principle for counting independent and dependent events. a. Use various counting models (including tree diagrams and lists) to identify the distinguishing factors of a context in which the Fundamental Counting Principle can be applied.
    Example: Apply the Fundamental Counting Principle in a context that can be represented by a tree diagram in which there are the same number of branches from each node at each level of the tree.
Link to Resource
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-stati…

CR Resource Type

Audio/Video

Resource Provider

Khan Academy
Accessibility

Accessibility

Video resources: includes closed captioning or subtitles
License

License Type

Custom

Custom License Type (URL)

https://www.khanacademy.org/about/tos

Comments or Notes

There are practice problems that students can complete after viewing the video.

habradley
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