# Cluster 2: Use probability to evaluate outcomes of decisions

General Information
Number: MAFS.912.S-MD.2
Title: Use probability to evaluate outcomes of decisions
Type: Cluster
Subject: Mathematics
Domain-Subdomain: Statistics & Probability: Using Probability to Make Decisions

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.912.S-MD.2.AP.7a
Identify and describe the degree to which something is rated “good” or “bad”/desirable or undesirable based on numerical information (Identify and describe the degree to which a decision/strategy is rated “good” or “bad"/desirable or undesirable based on numerical Information.).

## Related Resources

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

## Lesson Plans

Livestock Plans for Raising Red Nosed Reindeer:

This lesson about genetics and mutations investigates how red nosed reindeer could be raised in a livestock setting. Students will draw Punnett squares and design livestock plans for reproduction of red nosed reindeer.

Type: Lesson Plan

The Monty Hall Problem or How to Outsmart a Game Show and Win a Car:

This lesson teaches students how to make decisions in the face of uncertainty by using decision trees. It is aimed for high school kids with a minimal background in probability; the students only need to know how to calculate the probability of two uncorrelated events both occurring (ie flipping 2 heads in a row). Over the course of this lesson, students will learn about the role of uncertainty in decision making, how to make and use a decision tree, how to use limiting cases to develop an intuition, and how this applies to everyday life.

Type: Lesson Plan

Tree Diagrams and Probability:

This lesson is designed to develop students' ability to create tree diagrams and figure probabilities of events based on those diagrams. This lesson provides links to discussions and activities related to tree diagrams as well as suggested ways to work them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Lesson Plan

Modeling Conditional Probabilities 1: Lucky Dip:

This lesson unit is intended to help you assess how well students are able to understand conditional probability, represent events as a subset of a sample space using tables and tree diagrams, and communicate their reasoning clearly.

Type: Lesson Plan

Modeling Conditional Probabilities 2:

This lesson unit is intended to help you assess how well students understand conditional probability, and, in particular, to help you identify and assist students who have the following difficulties representing events as a subset of a sample space using tables and tree diagrams and understanding when conditional probabilities are equal for particular and general situations.

Type: Lesson Plan

Probability:

This lesson is designed to develop students' understanding of probability in real life situations. Students will also be introduced to running experiments, experimental probability, and theoretical probability. This lesson provides links to discussions and activities related to probability as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Lesson Plan

Phalangelpodscribitis? - Analysis with Probability:

Have you ever had a cold or some other ailment that was just a nuisance to you? You tried this medication and that medication in order to treat your self-diagnosis. However, when you have exhausted all your avenues, you find yourself at the Physician's office: paying the co-pay, getting a prescription, paying more to fill the prescription with hopes of not experiencing any of the side effects associated with the medicine, and if that particular medicine doesn't work, you are back at the doctor's office and switched to another.

Well, Phalangelpodscribitis is a recently diagnosed ailment that will put a person's feet in motion. It isn't contagious but the treatment can be intense. In this lesson students will be presented with seven (7) medications that will help cure an individual of Phalangelpodscribitis. Students will be given the effectiveness of each medication, the cost to patients with and without insurance, and the possible side effects of each. Each team will be tasked with ranking these medications for a client in order to help him decide the pros and cons of the medications that should be used in treating Phalangelpodscribitis (PPS).

Each team will be responsible for recording the procedure they used to rank the medications and to calculate the expected cost for the client when two medications must be administered since the first will prove ineffective for treatment alone. The team's suggestion brings results and the patient is cured!!

Time has passed and Phalangelpodscribitis, currently known as PPS, has returned. Oh no! What will your team suggest when the doctor begins to discuss the patient's mortality rate as it is associated with the medication?

Type: Lesson Plan

## 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

This lesson is designed to introduce students to statistical situations where the probabilities or outcomes might not be what is first expected. The lesson provides links to discussions and activities motivated by the idea of unexpected answers. Finally, the lesson provides links to follow-up lessons designed for use in succession with an introduction to probability and unexpected answers in probability.

## Teaching Ideas

The exercise detailed in this resource poses a paradox regarding birthdays. The question raised: how large does a group have to be in order to have a 50% or better probability that two or more people in the group share the same birthday? Intuitions about probability are challenged as students use their calculators to simulate random values to represent the birthdays and reach an answer.

Type: Teaching Idea

Conditional Probability and Probability of Simultaneous Events:

This lesson is designed to further students' practice with probability as well as introduce them to conditional probability and probabilities of simultaneous independent events. The lesson provides links to discussions and activities related to conditional and simultaneous probabilities as well as suggested ways to integrate them into the lesson. Finally, this lesson provides links to follow-up lessons designed for use in succession with this one.

Type: Teaching Idea

## Text Resource

Understanding Uncertainty: What Was the Probability of Obama Winning?:

This informational text resource is intended to support reading in the content area. The article examines various factors that changed the uncertainty of whether Barack Obama would win the 2008 election. Specifically,the article discusses probability, the science of quantifying uncertainty. The article questions common methods for assessing probability where symmetrical outcomes are assumed. Finally, the author explains how to use past evidence to assess the chances of future events.

Type: Text Resource

## Virtual Manipulatives

In this online activity, students burn a simulated forest and adjust the probability that the fire spreads from one tree to the other. This simulation also records data for each trial including the burn probability, where the fire started, the percent of trees burned, and how long the fire lasted. This activity allows students to explore the idea of chaos in a simulation of a realistic scenario. 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 are linked to the applet.

Type: Virtual Manipulative

Simple Monty Hall:

In this activity, students select one of three doors in an attempt to find a prize that is hidden behind one of them. After their first selection, one of the doors that doesn't have the prize behind it is revealed and the student has to decide whether to switch to the one remaining door or stay on the door of their first choice. This situation, referred to as the Monty Hall problem, was made famous on the show "Let's Make A Deal" with host Monty Hall. This activity allows students to explore the idea of conditional probability as well as unexpected probability. This activity includes 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

## Worksheet

Replacement and Probability:

This lesson is designed to develop students' understanding of sampling with and without replacement and its effects on the probability of drawing a desired object. The lesson provides links to discussions and activities related to replacement and probability as well as suggested ways to work them into the lesson. Finally, the lesson provides links to follow-up lessons that are designed to be used in succession with the current one.

Type: Worksheet

## Student Resources

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

## Virtual Manipulatives

In this online activity, students burn a simulated forest and adjust the probability that the fire spreads from one tree to the other. This simulation also records data for each trial including the burn probability, where the fire started, the percent of trees burned, and how long the fire lasted. This activity allows students to explore the idea of chaos in a simulation of a realistic scenario. 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 are linked to the applet.

Type: Virtual Manipulative

Simple Monty Hall:

In this activity, students select one of three doors in an attempt to find a prize that is hidden behind one of them. After their first selection, one of the doors that doesn't have the prize behind it is revealed and the student has to decide whether to switch to the one remaining door or stay on the door of their first choice. This situation, referred to as the Monty Hall problem, was made famous on the show "Let's Make A Deal" with host Monty Hall. This activity allows students to explore the idea of conditional probability as well as unexpected probability. This activity includes 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 topic.