Learn on PengienVision, Mathematics, Grade 7Chapter 7: Probability

Lesson 5: Determine Outcomes of Compound Events

In this Grade 7 lesson from enVision Mathematics, students learn how to identify the sample space of compound events — situations involving two or more combined events — using organized lists, tables, and tree diagrams. The lesson walks through examples such as mapping gender combinations for a three-child family, letter-number spinner pairings, and coin-and-number-cube outcomes to systematically count all possible results. By the end, students can confidently represent and count outcomes in a sample space for any compound event.

Section 1

Defining Simple and Compound Events

Property

A simple event is an event with a single outcome or consisting of one experiment. A compound event consists of two or more simple events.

Examples

  • Simple Event: Rolling a single six-sided die and getting a 4.
  • Simple Event: Flipping a coin and getting heads.
  • Compound Event: Rolling a die and flipping a coin.
  • Compound Event: Choosing a marble from a bag, and then choosing a second marble.

Explanation

Understanding the difference between simple and compound events is crucial for determining the correct way to calculate probabilities. A simple event involves just one action, like rolling one die or spinning one spinner. A compound event combines two or more of these simple actions, such as rolling two dice or flipping a coin three times. The methods for finding the total number of outcomes, like the Fundamental Counting Principle, apply specifically to compound events.

Section 2

Representing Sample Spaces with Organized Lists

Property

To list all possible outcomes in an experiment, systematically identify every distinct result that could occur. For experiments with multiple stages, use organized methods like tables, tree diagrams, or ordered lists to ensure no outcomes are missed or repeated.

Examples

Section 3

Representing Sample Spaces with Tables

Property

A two-way table organizes all possible outcomes of two events by listing the outcomes of the first event in rows and the outcomes of the second event in columns. Each cell represents one possible compound outcome, and the total number of outcomes equals the number of rows times the number of columns.

Examples

Book overview

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Chapter 7: Probability

  1. Lesson 1

    Lesson 1: Understand Likelihood and Probability

  2. Lesson 2

    Lesson 2: Understand Theoretical Probability

  3. Lesson 3

    Lesson 3: Understand Experimental Probability

  4. Lesson 4

    Lesson 4: Use Probability Models

  5. Lesson 5Current

    Lesson 5: Determine Outcomes of Compound Events

  6. Lesson 6

    Lesson 6: Find Probabilities of Compound Events

  7. Lesson 7

    Lesson 7: Simulate Compound Events

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Defining Simple and Compound Events

Property

A simple event is an event with a single outcome or consisting of one experiment. A compound event consists of two or more simple events.

Examples

  • Simple Event: Rolling a single six-sided die and getting a 4.
  • Simple Event: Flipping a coin and getting heads.
  • Compound Event: Rolling a die and flipping a coin.
  • Compound Event: Choosing a marble from a bag, and then choosing a second marble.

Explanation

Understanding the difference between simple and compound events is crucial for determining the correct way to calculate probabilities. A simple event involves just one action, like rolling one die or spinning one spinner. A compound event combines two or more of these simple actions, such as rolling two dice or flipping a coin three times. The methods for finding the total number of outcomes, like the Fundamental Counting Principle, apply specifically to compound events.

Section 2

Representing Sample Spaces with Organized Lists

Property

To list all possible outcomes in an experiment, systematically identify every distinct result that could occur. For experiments with multiple stages, use organized methods like tables, tree diagrams, or ordered lists to ensure no outcomes are missed or repeated.

Examples

Section 3

Representing Sample Spaces with Tables

Property

A two-way table organizes all possible outcomes of two events by listing the outcomes of the first event in rows and the outcomes of the second event in columns. Each cell represents one possible compound outcome, and the total number of outcomes equals the number of rows times the number of columns.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 7: Probability

  1. Lesson 1

    Lesson 1: Understand Likelihood and Probability

  2. Lesson 2

    Lesson 2: Understand Theoretical Probability

  3. Lesson 3

    Lesson 3: Understand Experimental Probability

  4. Lesson 4

    Lesson 4: Use Probability Models

  5. Lesson 5Current

    Lesson 5: Determine Outcomes of Compound Events

  6. Lesson 6

    Lesson 6: Find Probabilities of Compound Events

  7. Lesson 7

    Lesson 7: Simulate Compound Events