# MAFS.7.SP.3.8

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
1. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
2. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
3. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
General Information
Subject Area: Mathematics
Domain-Subdomain: Statistics & Probability
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Investigate chance processes and develop, use, and evaluate probability models. (Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications
Assessed with:
MAFS.7.SP.3.7

Sample Test Items (1)
• Test Item #: Sample Item 1
• Question:

Tony has a bucket filled with green, blue, yellow, and red markers. He removes 3 markers from the bucket, with replacement.

Select all the outcomes that are possible.

• Difficulty: N/A
• Type: MS: Multiselect

## Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205050: M/J Grade 7 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.7.SP.3.AP.8a: Determine the theoretical probability of compound events (e.g., two coins or two dice).
MAFS.7.SP.3.AP.8b: Use tree diagrams, frequency tables, organized lists, and/or simulations to collect data from a two-step simulation of compound events (using two coins and/or two dice).

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Assessments

Sample 3 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 4 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 2 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 1 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

## Formative Assessments

Work Clothing:

Students are asked to make a tree diagram to determine all possible outcomes of a compound event.

Type: Formative Assessment

Number List:

Students are asked to make an organized list that displays all possible outcomes of a compound event.

Type: Formative Assessment

Coat Count:

Students are asked to design a simulation to generate frequencies for complex events.

Type: Formative Assessment

Automotive Probabilities:

Students are asked to find the probability of a compound event using a tree diagram and explain how the tree diagram was used to find the probability.

Type: Formative Assessment

## Lesson Plans

Pick and Roll:

This lesson is designed to teach students about independent and dependent compound probability and give students opportunities to experiment with probabilities through the use of manipulatives, games, and a simulation project. The lesson can take as long as three hours (classes), but can be modified to fit within two hours (classes).

Type: Lesson Plan

Independent Compound Probability:

During this lesson, students will use Punnett Squares to determine the probability of an offspring's characteristics.

Type: Lesson Plan

Understanding Probability of Compound Events:

This lesson uses guided teaching, small group activities, and student creations all-in-one! Students will be able to solve and create compound event word problems. They will also be able to identify what type of event is being used in a variety of word problems.

Type: Lesson Plan

Permutations and Combinations:

This is a seventh grade lesson that should follow a lesson on simple probability. This is a great introduction to compound probability and a fun, hands-on activity that allows students to explore the differences between permutations and combinations.  This activity leads into students identifying situations involving combinations and permutations in a real-world context.

Type: Lesson Plan

How to Hit it Big in the Lottery - Probability of Compound Events:

Students will explore a wide variety of interesting situations involving probability of compound events. Students will learn about independent and dependent events and their related probabilities.

Lesson includes:

• Bell-work that reviews prerequisite knowledge
• Directions for a great In-Your-Seat Game that serves as an interest builder/introduction
• Vocabulary
• Built-in Kagan Engagement ideas
• An actual lottery activity for real-life application

Type: Lesson Plan

Chancy Candy:

In this lesson students will use candy to find the probability of independent compound events, determining the sample space from a tree diagram. They will then do an experiment to test the theoretical probability. Once the experiment is complete, the students will compare the theoretical and experimental probability.

Type: Lesson Plan

## Original Student Tutorial

Alice in Mathematics-Land:

Help Alice discover that compound probabilities can be determined through calculations or by drawing tree diagrams in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Experts

Let's Make a Math Deal:

Should I keep my choice or switch?  Learn more about the origins and probability behind the Monty Hall door picking dilemma and how Game Theory and strategy effect the probability.

Type: Perspectives Video: Expert

History of Probability and the Problem of Points:

What was the first question that started probability theory?

Type: Perspectives Video: Expert

Waiting Times:

As the standards in statistics and probability unfold, students will not yet know the rules of probability for compound events. Thus, simulation is used to find an approximate answer to these questions. In fact, part b would be a challenge to students who do know the rules of probability, further illustrating the power of simulation to provide relatively easy approximate answers to wide-ranging problems.

Rolling Twice:

The purpose of this task is for students to compute the theoretical probability of a compound event. Teachers may wish to emphasize the distinction between theoretical and experimental probabilities for this problem. For students learning to distinguish between theoretical and experimental probability, it would be good to find an experimental probability either before or after students have calculated the theoretical probability.

Sitting Across From Each Other:

The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.

## Tutorials

Compound Sample Spaces:

This video explores how to create sample spaces as tree diagrams, lists and tables.

Type: Tutorial

Probability of Compound Events:

This video shows how to use a sample space diagram to find probability.

Type: Tutorial

Die Rolling Probability:

Use a table to find the probability of a compound event.

Type: Tutorial

Count Outcomes Using a Tree Diagram:

This video shows an example of using a tree diagram to find the probability of a compound event.

Type: Tutorial

## Video/Audio/Animation

Compound Probability of Independent Events:

This 6-minute video provides an example of how to work with compound probability of independent events through the example of flipping a coin. If you flip a coin and it lands on heads, is the next flip more likely to be tails? Or are those events independent?

Type: Video/Audio/Animation

## Virtual Manipulatives

Hamlet Happens:

The purpose of this manipulative is to help students recognize that (1) unusual events do happen, and (2) it may take a longer time for some of them to happen. The letters are drawn at random from the beginning of Hamlet's soliloquy, "To be, or not to be." Any word made from those letters (such as TO) can be entered in the box. When the start is pressed, letters are drawn and recorded. The process continues until the word appears.

Type: Virtual Manipulative

Interactive Marbles:

This online manipulative allows the student to simulate placing marbles into a bag and finding the probability of pulling out certain combinations of marbles. This allows exploration of probabilities of multiple events as well as probability with and without replacement. The tabs above the applet provide access to supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

Type: Virtual Manipulative

## MFAS Formative Assessments

Automotive Probabilities:

Students are asked to find the probability of a compound event using a tree diagram and explain how the tree diagram was used to find the probability.

Coat Count:

Students are asked to design a simulation to generate frequencies for complex events.

Number List:

Students are asked to make an organized list that displays all possible outcomes of a compound event.

Work Clothing:

Students are asked to make a tree diagram to determine all possible outcomes of a compound event.

## Original Student Tutorials Mathematics - Grades 6-8

Alice in Mathematics-Land:

Help Alice discover that compound probabilities can be determined through calculations or by drawing tree diagrams in this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorial

Alice in Mathematics-Land:

Help Alice discover that compound probabilities can be determined through calculations or by drawing tree diagrams in this interactive tutorial.

Type: Original Student Tutorial

Waiting Times:

As the standards in statistics and probability unfold, students will not yet know the rules of probability for compound events. Thus, simulation is used to find an approximate answer to these questions. In fact, part b would be a challenge to students who do know the rules of probability, further illustrating the power of simulation to provide relatively easy approximate answers to wide-ranging problems.

Rolling Twice:

The purpose of this task is for students to compute the theoretical probability of a compound event. Teachers may wish to emphasize the distinction between theoretical and experimental probabilities for this problem. For students learning to distinguish between theoretical and experimental probability, it would be good to find an experimental probability either before or after students have calculated the theoretical probability.

Sitting Across From Each Other:

The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.

## Tutorials

Compound Sample Spaces:

This video explores how to create sample spaces as tree diagrams, lists and tables.

Type: Tutorial

Probability of Compound Events:

This video shows how to use a sample space diagram to find probability.

Type: Tutorial

Die Rolling Probability:

Use a table to find the probability of a compound event.

Type: Tutorial

Count Outcomes Using a Tree Diagram:

This video shows an example of using a tree diagram to find the probability of a compound event.

Type: Tutorial

## Video/Audio/Animation

Compound Probability of Independent Events:

This 6-minute video provides an example of how to work with compound probability of independent events through the example of flipping a coin. If you flip a coin and it lands on heads, is the next flip more likely to be tails? Or are those events independent?

Type: Video/Audio/Animation

## Virtual Manipulatives

Hamlet Happens:

The purpose of this manipulative is to help students recognize that (1) unusual events do happen, and (2) it may take a longer time for some of them to happen. The letters are drawn at random from the beginning of Hamlet's soliloquy, "To be, or not to be." Any word made from those letters (such as TO) can be entered in the box. When the start is pressed, letters are drawn and recorded. The process continues until the word appears.

Type: Virtual Manipulative

Interactive Marbles:

This online manipulative allows the student to simulate placing marbles into a bag and finding the probability of pulling out certain combinations of marbles. This allows exploration of probabilities of multiple events as well as probability with and without replacement. The tabs above the applet provide access to supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

Type: Virtual Manipulative

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Waiting Times:

As the standards in statistics and probability unfold, students will not yet know the rules of probability for compound events. Thus, simulation is used to find an approximate answer to these questions. In fact, part b would be a challenge to students who do know the rules of probability, further illustrating the power of simulation to provide relatively easy approximate answers to wide-ranging problems.

Rolling Twice:

The purpose of this task is for students to compute the theoretical probability of a compound event. Teachers may wish to emphasize the distinction between theoretical and experimental probabilities for this problem. For students learning to distinguish between theoretical and experimental probability, it would be good to find an experimental probability either before or after students have calculated the theoretical probability.

Sitting Across From Each Other:

The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.