# Standard 2: Develop an understanding of probability. Find and compare experimental and theoretical probabilities.

General Information
Number: MA.7.DP.2
Title: Develop an understanding of probability. Find and compare experimental and theoretical probabilities.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.7.DP.2.AP.1
Use tree diagrams, frequency tables, organized lists, and/or simulations to collect data from a simple experiment.
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.
MA.7.DP.2.AP.3
Determine the theoretical probability of a simple chance event.
MA.7.DP.2.AP.4
Conduct a simple experiment to find experimental probabilities.

## Related Resources

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

## Formative Assessments

Hen Eggs:

Students are asked to estimate the probability of a chance event based on observed frequencies.

Type: Formative Assessment

Game of Chance:

Students are asked to estimate the frequency of an event given its probability and explain why an expected frequency might differ from an observed frequency.

Type: Formative Assessment

Marble Probability:

Students are asked to determine probabilities based on observed outcomes and to determine if the outcomes appear to be equally likely.

Type: Formative Assessment

Number Cube:

Students are asked to determine probabilities based on observed outcomes and to determine if the outcomes appear to be equally likely.

Type: Formative Assessment

Probability or Not?:

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

Type: Formative Assessment

Technical Difficulties:

Students are given a scenario and asked to determine the probability of two different events.

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

Errand Runner:

Students are asked to determine the probability of a chance event and explain possible causes for the difference between the probability and observed frequencies.

Type: Formative Assessment

## Lesson Plans

Probability of Being Summoned for Jury Duty:

Students will explore how an individual’s personal experience may impact their interpretation of the likelihood of a specific event by comparing theoretical and experimental probabilities in the context of being summoned for jury duty in this integrated lesson.

Type: Lesson Plan

Experimental and Theoretical Probability:

Students will compare experimental and theoretical probability using a standard deck of cards.  Then, given fictional data from the population of 3 counties in Florida, they will compare the theoretical probability of an individual being summoned for jury service in each county to the experimental probability based on individual experiences.  Finally, students will evaluate the impact of sample size on this comparison and explore the importance of a random jury summons process in our judicial system in this integrated lesson.

Type: Lesson Plan

What is the Likelihood?:

Students will develop an understanding of likelihood based on calculated probabilities and relate these concepts to being called for jury duty in this integrated lesson.

Type: Lesson Plan

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

The Debate: Who is a Better Baller?:

In this activity the students will use NBA statistics on Lebron James and Tim Duncan who were key players in the 2014 NBA Finals, to calculate, compare, and discuss mean, median, interquartile range, variance, and standard deviation. They will also construct and discuss box plots.

Type: Lesson Plan

Casino Royale:

Students examine games of chance to determine the difference between dependent and independent conditional probability.

Type: Lesson Plan

Computer Simulated Experiments in Genetics:

A computer simulation package called "Star Genetics" is used to generate progeny for one or two additional generations. The distribution of the phenotypes of the progeny provide data from which the parental genotypes can be inferred. The number of progeny can be chosen by the student in order to increase the student's confidence in the inference.

Type: Lesson Plan

Selecting a Sample Population:

The student explores several strategies for selecting a sample population to support making inferences about the population.

Type: Lesson Plan

Generating Multiple Samples to Gauge Variation:

Students explore variation in random samples and use random samples to make generalizations about the population.

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 conduct an experiment to test the theoretical probability. Once the experiment is complete, the students will compare the theoretical and experimental probability.

Type: Lesson Plan

When Pigs Fly:

In this lesson students will explore probability and likelihood that an event will occur. They will place both serious and silly events on a number line, once they have assigned a value to that event. They will work with a group and then justify their classifications to their peers.

Type: Lesson Plan

Practically Probable:

In this lesson, students will differentiate between likely and unlikely event, as well as learn the difference between dependent and independent events. Finally, they learn how to compute theoretical probabilities in simple experiments.

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 75Âº 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

This activity will allow students to explore the concept of simple probability using a random selection of multi-colored beads.

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

Probabilistic Weather Modeling:

Meteorologist from Risk Management discusses the use of probability in predicting hurricane tracks.

Type: Perspectives Video: Expert

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

The Titanic 1:

This task asks students to calculate probabilities using information presented in a two-way frequency table.

Tossing Cylinders:

The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data. The cylindrical objects used in this task typically have three different resting positions but not all of these may be equally likely and some may be extremely unlikely or impossible when the object is tossed. Furthermore, obtaining the probabilities of the outcomes is perhaps only possible through the use of long-run relative frequencies. This is because these cylinders do not have the same types of symmetries as objects that are often used as dice, such as cubes or tetrahedrons, where each outcome is equally likely.

Election Poll, Variation 3:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 3 introduces technology and encourages students to use a random number generator or statistics software to generate a random sample of student responses and to simulate a distribution of sample proportions from a population with 50% successes.

How Many Buttons?:

This resource involves a simple data-gathering activity which furnishes data that students organize into a table. They are then asked to refer to the data and determine the probability of various outcomes.

Election Poll, Variation 2:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 2 leads students through a physical simulation for generating sample proportions by sampling, and re-sampling, marbles from a box.

Rolling Dice:

This task is intended as a classroom activity. Students pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.

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.

## 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

## Tutorials

Finding Probability:

This video demonstrates several examples of finding probability of random events.

Type: Tutorial

The Limits of Probability:

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

Type: Tutorial

Comparing Theoretical to Experimental Probabilites:

This video compares theoretical and experimantal probabilities and sources of possible discrepancy.

Type: Tutorial

Finding Probability of a Simple Event:

This video demonstrates how to find the probability of a simple event.

Type: Tutorial

Making Predictions with Probability:

Watch the video as it predicts the number of times a spinner will land on a given outcome.

Type: Tutorial

## Student Resources

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

## 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

The Titanic 1:

This task asks students to calculate probabilities using information presented in a two-way frequency table.

Tossing Cylinders:

The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data. The cylindrical objects used in this task typically have three different resting positions but not all of these may be equally likely and some may be extremely unlikely or impossible when the object is tossed. Furthermore, obtaining the probabilities of the outcomes is perhaps only possible through the use of long-run relative frequencies. This is because these cylinders do not have the same types of symmetries as objects that are often used as dice, such as cubes or tetrahedrons, where each outcome is equally likely.

How Many Buttons?:

This resource involves a simple data-gathering activity which furnishes data that students organize into a table. They are then asked to refer to the data and determine the probability of various outcomes.

Election Poll, Variation 2:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 2 leads students through a physical simulation for generating sample proportions by sampling, and re-sampling, marbles from a box.

Rolling Dice:

This task is intended as a classroom activity. Students pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.

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

Finding Probability:

This video demonstrates several examples of finding probability of random events.

Type: Tutorial

The Limits of Probability:

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

Type: Tutorial

Comparing Theoretical to Experimental Probabilites:

This video compares theoretical and experimantal probabilities and sources of possible discrepancy.

Type: Tutorial

Finding Probability of a Simple Event:

This video demonstrates how to find the probability of a simple event.

Type: Tutorial

Making Predictions with Probability:

Watch the video as it predicts the number of times a spinner will land on a given outcome.

Type: Tutorial

## Parent Resources

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

The Titanic 1:

This task asks students to calculate probabilities using information presented in a two-way frequency table.

Tossing Cylinders:

The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data. The cylindrical objects used in this task typically have three different resting positions but not all of these may be equally likely and some may be extremely unlikely or impossible when the object is tossed. Furthermore, obtaining the probabilities of the outcomes is perhaps only possible through the use of long-run relative frequencies. This is because these cylinders do not have the same types of symmetries as objects that are often used as dice, such as cubes or tetrahedrons, where each outcome is equally likely.

How Many Buttons?:

This resource involves a simple data-gathering activity which furnishes data that students organize into a table. They are then asked to refer to the data and determine the probability of various outcomes.

Election Poll, Variation 2:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 2 leads students through a physical simulation for generating sample proportions by sampling, and re-sampling, marbles from a box.