 # Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities

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Lesson Plans and Worksheets for Grade 7
Lesson Plans and Worksheets for all Grades

Examples, videos, and solutions to help Grade 7 students learn how to determine the possible outcomes for simple chance experiments.

New York State Common Core Math Grade 7, Module 5, Lesson 6
Grade 7, Module 5, Lesson 6 Worksheets

### Lesson 6 Student Outcomes

• Given a description of a chance experiment that can be thought of as being performed in two or more stages, students use tree diagrams to organize and represent the outcomes in the sample space.  Students calculate probabilities of compound events.

### Lesson 6 Summary

Tree diagrams can be used to organize outcomes in the sample space for chance experiments that can be thought of as being performed in multiple stages. Tree diagrams are also useful for computing probabilities of events with more than one outcome.

Lesson 6 Classwork

Example 1: Two Nights of Games Imagine that a family decides to play a game each night. They all agree to use a tetrahedral die (i.e., a four-sided pyramidal die where each of four possible outcomes is equally likely—see image on page 9) each night to randomly determine if they will play a board game ( ) or a card game ( ). The tree diagram mapping the possible overall outcomes over two consecutive nights will be developed below. To make a tree diagram, first present all possibilities for the first stage. (In this case, Monday.)

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