Learn on PengiReveal Math, AcceleratedUnit 10: Probability

Lesson 10-5: Probability of Compound Events

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to find the theoretical probability of compound events by identifying all possible outcomes in a sample space. Students practice using organized tools such as tree diagrams and tables to list outcomes when two or more simple events are combined, such as multiple coin flips or spinning two spinners. The lesson reinforces the concept that probability is the ratio of favorable outcomes to total outcomes in the sample space.

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 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

Section 3

Creating Tree Diagrams for Compound Events

Property

A tree diagram systematically displays all possible outcomes of compound events by creating branches for each outcome of the first event, then extending branches for each outcome of subsequent events from every existing branch.

Examples

Book overview

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Continue this chapter

Unit 10: Probability

  1. Lesson 1

    Lesson 10-1: Understand Probability

  2. Lesson 2

    Lesson 10-2: Experimental Probability of Simple Events

  3. Lesson 3

    Lesson 10-3: Theoretical Probability of Simple Events

  4. Lesson 4

    Lesson 10-4: Compare Probabilities of Simple Events

  5. Lesson 5Current

    Lesson 10-5: Probability of Compound Events

  6. Lesson 6

    Lesson 10-6: Simulate Chance 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 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

Section 3

Creating Tree Diagrams for Compound Events

Property

A tree diagram systematically displays all possible outcomes of compound events by creating branches for each outcome of the first event, then extending branches for each outcome of subsequent events from every existing branch.

Examples

Book overview

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

Continue this chapter

Unit 10: Probability

  1. Lesson 1

    Lesson 10-1: Understand Probability

  2. Lesson 2

    Lesson 10-2: Experimental Probability of Simple Events

  3. Lesson 3

    Lesson 10-3: Theoretical Probability of Simple Events

  4. Lesson 4

    Lesson 10-4: Compare Probabilities of Simple Events

  5. Lesson 5Current

    Lesson 10-5: Probability of Compound Events

  6. Lesson 6

    Lesson 10-6: Simulate Chance Events