# Cluster 2: Use the rules of probability to compute probabilities of compound events in a uniform probability model. (Algebra 2 - Additional 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.

General Information
Number: MAFS.912.S-CP.2
Title: Use the rules of probability to compute probabilities of compound events in a uniform probability model. (Algebra 2 - Additional Cluster)
Type: Cluster
Subject: Mathematics
Domain-Subdomain: Statistics & Probability: Conditional Probability & the Rules of Probability

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.912.S-CP.2.AP.6a
Using a two-way table, find the conditional probability of A given within the context of the model.
MAFS.912.S-CP.2.AP.7a
Use the addition rule, P(A or B) = P(A) + P(B) – P(A and B).
MAFS.912.S-CP.2.AP.7b
Interpret the answer to the Addition Rule within the context of the model.

## Related Resources

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

## Assessments

Sample 4 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 3 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

## Lesson Plan

Medical Testing:

This lesson unit is intended to help you assess how well students are able to:

• make sense of a real life situation and decide what math to apply to the problem
• understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model
• represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams
• interpret the results and communicate their reasoning clearly

Type: Lesson Plan

## Perspectives Video: Expert

History of Probability and the Problem of Points:

WhatÂ was the first question that started probability theory?

Type: Perspectives Video: Expert

Rain and Lightning:

This problem solving task challenges students to determine if two weather events are independent, and use that conclusion to find the probability of having similar weather events under certain conditions.

The task is intended to address sample space, independence, probability distributions and permutations/combinations.

Alex, Mel, and Chelsea Play a Game:

This task combines the concept of independent events with computational tools for counting combinations, requiring fluent understanding of probability in a series of independent events.

Coffee at Mom's Diner:

This task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context.

How Do You Get to School?:

This task requires students to use information in a two-way table to calculate a probability and a conditional probability.

The Titanic 2:

This task lets students explore the concepts of probability as a fraction of outcomes and using two-way tables of data.

The Titanic 1:

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

Random Walk III:

The task provides a context to calculate discrete probabilities and represent them on a bar graph.

Random Walk IV:

This problem solving task gives a situation where the numbers are too large to calculate, so abstract reasoning is required in order to compare the different probabilities.

The Titanic 3:

This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic by consulting a table of data.

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 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

The Logic of Drug Testing:

This informational text resource is intended to support reading in the content area. This article explores the reliability of drug tests for athletes, using mathematics. The author attempts to address this issue by relating drug tests to conditional probability. Throughout the text, various numbers that affect the calculation of a reliable probability are discussed. Numbers such as test sensitivity, test specificity, and weight of evidence are related to Bayes' theorem, which is ultimately used to calculate the conditional probability.

Type: Text Resource

## Tutorial

Compound Probability with Dependent Events:

This video describes using multiplication to find the compound probability of dependent events.

Type: Tutorial

## 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.

Rain and Lightning:

This problem solving task challenges students to determine if two weather events are independent, and use that conclusion to find the probability of having similar weather events under certain conditions.

The task is intended to address sample space, independence, probability distributions and permutations/combinations.

Alex, Mel, and Chelsea Play a Game:

This task combines the concept of independent events with computational tools for counting combinations, requiring fluent understanding of probability in a series of independent events.

Coffee at Mom's Diner:

This task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context.

The Titanic 2:

This task lets students explore the concepts of probability as a fraction of outcomes and using two-way tables of data.

The Titanic 1:

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

Random Walk III:

The task provides a context to calculate discrete probabilities and represent them on a bar graph.

Random Walk IV:

This problem solving task gives a situation where the numbers are too large to calculate, so abstract reasoning is required in order to compare the different probabilities.

The Titanic 3:

This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic by consulting a table of data.

## Tutorial

Compound Probability with Dependent Events:

This video describes using multiplication to find the compound probability of dependent events.

Type: Tutorial

## Parent Resources

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

Rain and Lightning:

This problem solving task challenges students to determine if two weather events are independent, and use that conclusion to find the probability of having similar weather events under certain conditions.

The task is intended to address sample space, independence, probability distributions and permutations/combinations.

Alex, Mel, and Chelsea Play a Game:

This task combines the concept of independent events with computational tools for counting combinations, requiring fluent understanding of probability in a series of independent events.

Coffee at Mom's Diner:

This task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context.

The Titanic 2:

This task lets students explore the concepts of probability as a fraction of outcomes and using two-way tables of data.

The Titanic 1:

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

Random Walk III:

The task provides a context to calculate discrete probabilities and represent them on a bar graph.