# MA.7.DP.2.2 Export Print
Given the probability of a chance event, interpret the likelihood of it occurring. Compare the probabilities of chance events.

### Clarifications

Clarification 1: Instruction includes representing probability as a fraction, percentage or decimal between 0 and 1 with probabilities close to 1 corresponding to highly likely events and probabilities close to 0 corresponding to highly unlikely events.

Clarification 2: Instruction includes P(event) notation.

Clarification 3: Instruction includes representing probability as a fraction, percentage or decimal.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Event
• Theoretical Probability

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 7, students interpret the probability of a chance event and the likelihood of it occurring. In grade 8, students will solve problems involving probabilities related to single or repeated experiments, including making predictions based on theoretical probability.
• An event is a set of outcomes.
• For example, if the experiment is to roll a six-sided die, possible events could be:
• “rolling a 3 or a 4;”
• “rolling an even number;” or
• “not rolling a 2.”
• Instruction includes the understanding that some events can have a probability of 1 or 0. Students should understand that if an event has a probability of zero, the event is impossible or will not occur. If an event has a probability of one, the event is certain or must occur.
• For example, in the experiment of rolling a 6-sided die, the event of rolling a 1, 2, 3, 4, 5 or 6 would have a probability of 1.
• For example, when rolling a 6-sided fair die, the event of rolling a 7 would have a probability of 0.
• Instruction includes having students use probabilities of 1, 0.5 and 0 as benchmark probabilities to interpret the likelihood of other events.
• For example, if a student wants to interpret the likelihood represented by the probability of 80%, they can compare 80% to the benchmark probabilities of 50% and 100%.
• If an event has a probability of 0.5, it can be interpreted that is has the same likelihood as its opposite.
• For example, in the experiment of picking a card from a standard 52-card deck, the event of picking a red card has a probability of 0.5, which can be interpreted as having the same likelihood as the opposite event, which is picking a black card.

### Common Misconceptions or Errors

• Students may invert the meaning of an event and an experiment.
• Students may confuse the mathematical meaning of a word like “event” with the everyday meaning.
• Students may incorrectly convert forms of probability between fractions and percentages. To address this misconception, scaffold with more familiar values initially to facilitate the interpretation.
• Students may incorrectly interpret a value with a negative sign as a possible probability.
• For example, −$\frac{\text{1}}{\text{2}}$ cannot represent a probability since negative values are less than 0.

### Strategies to Support Tiered Instruction

• Teacher creates and posts an anchor chart with visual representations of probability terms to assist students in correct academic vocabulary when solving real-world problems.
• Teacher provides opportunities for students to use a 100 frame to review place value for and the connections to decimal, fractional and percentage forms of probabilities.
• Instruction includes the use of a 100 frame to review place value for tenths, hundredths, and if needed, thousandths and the connections for decimal and fractional forms of probabilities.
• When students incorrectly convert from one form to another (i.e, fraction to percentage), the teacher scaffolds with more familiar values initially to facilitate the interpretation.

Determine which of the following could represent the probability of an event. For those that can, provide a possible event that would fit the probability given. ### Instructional Items

Instructional Item 1
In each scenario, a probability is given. Describe each event as likely, unlikely or neither.
• a. The probability of a hurricane being within 100 miles of a location in two days is 40%.
• b. The probability of a thunderstorm being located within 5 miles of your house sometime tomorrow is $\frac{\text{9}}{\text{10}}$
• c. The probability of a given baseball player getting at least three hits in the game today is 0.08.

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.7.DP.2.AP.2: Given the probability of a simple chance event written as a fraction, percentage or decimal between 0 and 1, determine how likely is it that an event will occur.

## Related Resources

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

## Formative Assessments

Probability or Not?:

Students are asked to determine whether or not a given number could represent the probability of an event.

Type: Formative Assessment

Likely or Unlikely?:

Students are asked to determine the likelihood of an event given a probability.

Type: Formative Assessment

Likelihood of an Event:

Students are asked to determine the likelihood of an event given a probability.

Type: Formative Assessment

## Lesson Plans

Genetics Has Gone to the Dogs!:

This lesson uses pooches to teach about pedigrees and the impact of artificial selection on individuals and populations as well as to drive home math concepts already discussed in lessons on Punnet squares.

Type: Lesson Plan

Genetics can be a Monster!:

In this lesson, students will use Punnett squares to calculate the probabilities of different genotypes and phenotypes produced by genetic crosses.

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

Planning the perfect wedding:

Students will decide what is the best month to celebrate an outdoor wedding. The couple is looking for the perfect wedding day. What is the definition of a perfect day? It has to be a Saturday or Sunday with a 20% or less probability of rain and sunny but not too hot. Based on the information provided , students will find the month in which the probability of having a rainy day and the probability of having a super hot day (temperature higher than 75º F) are minimal.

Type: Lesson Plan

Probabilities and Punnett Squares:

Students simulate the process of meiosis for an alien society. The students choose physical characteristics for hair, nose and eyes corresponding to genes and then generate two alien babies. Then pictures of the parents and babies are drawn, with similarities and differences noted and explained.

Type: Lesson Plan

Introduction to Probability:

This resource is designed to introduce students to the concept of probability: the probability of a rare event is represented by a positive number close to zero, the probability of a nearly certain event occurring is represented by a positive number slightly less than one. Students will indicate the approximate probability of events on a number line and determine which events are more likely than others.

Type: Lesson Plan

## Original Student Tutorial

Introduction to Probability:

Learn how to calculate the probability of simple events, that probability is the likeliness of an event occurring, and that some events may be more likely than others to occur in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Experts

How Math Models Help Insurance Companies After a Hurricane Hits:

Hurricanes can hit at any time! How do insurance companies use math and weather data to help to restore the community?

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

## Text Resource

Shuffling Shenanigans:

This informational text resource is intended to support reading in the content area. A student in love with magic card tricks asks and answers his own math questions after pursuing a career as a mathematician in order to solve them. How many times must a deck be shuffled to achieve a truly random mix of cards? The answer lies within.

Type: Text Resource

## Tutorial

The Limits of Probability:

This video discusses the limits of probability as between 0 and 1.

Type: Tutorial

## STEM Lessons - Model Eliciting Activity

Planning the perfect wedding:

Students will decide what is the best month to celebrate an outdoor wedding. The couple is looking for the perfect wedding day. What is the definition of a perfect day? It has to be a Saturday or Sunday with a 20% or less probability of rain and sunny but not too hot. Based on the information provided , students will find the month in which the probability of having a rainy day and the probability of having a super hot day (temperature higher than 75º F) are minimal.

## MFAS Formative Assessments

Likelihood of an Event:

Students are asked to determine the likelihood of an event given a probability.

Likely or Unlikely?:

Students are asked to determine the likelihood of an event given a probability.

Probability or Not?:

Students are asked to determine whether or not a given number could represent the probability of an event.

## Original Student Tutorials Mathematics - Grades 6-8

Introduction to Probability:

Learn how to calculate the probability of simple events, that probability is the likeliness of an event occurring, and that some events may be more likely than others to occur in this interactive tutorial.

## Student Resources

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

## Original Student Tutorial

Introduction to Probability:

Learn how to calculate the probability of simple events, that probability is the likeliness of an event occurring, and that some events may be more likely than others to occur in this interactive tutorial.

Type: Original Student Tutorial

## Tutorial

The Limits of Probability:

This video discusses the limits of probability as between 0 and 1.

Type: Tutorial

## Parent Resources

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