# Lesson 8

Keeping Track of All Possible Outcomes

### Lesson Narrative

In this lesson, students practice listing the sample space for a compound event. They make use of the structure (MP7) of tree diagrams, tables, and organized lists as methods of organizing this information. Students notice that the total number of outcomes in the sample space for an experiment that can be thought of as being performed as a sequence of steps can be found by multiplying the number of possible outcomes for each step in the experiment (MP8).

In the next lesson, students will use sample spaces to calculate the probability of compound events.

### Learning Goals

Teacher Facing

• Compare and contrast (in writing) different methods for representing the sample space of a compound event, and evaluate (orally) their usefulness.
• Determine the total number of possible outcomes for a compound event, and justify the reasoning (orally, in writing, and using other representations).
• Interpret or create a list, table, or tree diagram that represents the sample space of a compound event.

### Student Facing

Let’s explore sample spaces for experiments with multiple parts.

### Student Facing

• I can write out the sample space for a multi-step experiment, using a list, table, or tree diagram.