unit 8 probability and statistics homework 5 compound probability

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Compound probability is a concept that relates the likelihood of two independent (i.e., unconnected) events occurring. To determine compound probability, you multiply the probability of the first event by the probability of the second event. In these worksheets, students will learn to determine the probability of an outcome and the number of possible outcomes of an event. Your students will find the probability of given sets of probable outcomes. They will find the probability of each potential outcome. They will find the probability of both single and multiple events. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. It also contains ample worksheets for students to practice the skills independently. When finished with this set of worksheets, students will be able to determine the probability of an outcome and the number of possible outcomes of an event.

These worksheets explain how to determine the probability of an outcome and the number of possible outcomes of an event. Sample problems are solved and practice problems are provided.

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Compound probability worksheets, click the buttons to print each worksheet and answer key..

This worksheet explains how to list the possible outcomes of a described experiment. A sample problem is solved.

Lesson and Practice

Students will learn how to find the probability of a set of possible outcomes. A sample problem is solved and two practice problems are provided.

Practice Worksheet

Students will find the probability of each potential outcome. Ten problems are provided.

Lesson Practice Worksheet

Students will practice finding the probability of potential outcomes. Ten problems are provided.

Compound Probability Drills

Students will find the probability of each potential outcome. Eight problems are provided.

Students will warm up by finding the probability of each potential outcome. Three problems are provided.

Single and Compound Events Lesson

This worksheet explains how to determine the probability of a single event. A sample problem is solved, and two practice problems are provided.

Single and Compound Events Worksheet

Students will determine the probability of the events described. Ten problems are provided.

Single and Compound Events Practice

Students will practice determining the probability of the events described. Ten problems are provided.

Single and Compound Events Review and Practice

The concept of how to determine probability is reviewed. A sample problem is solved and six practice problems are provided.

Single and Compound Events Quiz

Students will demonstrate their proficiency in determining probability. Ten problems are provided.

Single and Compound Events Check

Students will determine the probability of the events described. Three problems are provided, and space is included for students to copy the correct answer when given.

Working with Single and Compound Events Lesson

This worksheet explains how to determine the number of possible outcomes to a situation. A sample problem is solved, and two practice problems are provided.

Working with Single and Compound Events Worksheet

Students will determine the probability of each event. Ten problems are provided.

Working with Single and Compound Events Practice

Students will practice determining the probability of each event. Ten problems are provided.

Working with Single and Compound Events Review and Practice

The concept of how to determine the probability of an event is reviewed. A sample problem is solved and six practice problems are provided.

Working with Single and Compound Events Quiz

Students will demonstrate their proficiency in determining the probability of an event. Ten problems are provided.

Working with Single and Compound Events Check

Students will determine the probability of each event. Three problems are provided, and space is included for students to copy the correct answer when given.

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Unit 8 – Probability

Probability Terminology

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Compound Events

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Sums of Dice

Simulating Compound Events

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Unit 8 Mid-Unit Quiz – Form A

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U08.AO.01 – Compound Probability Practice

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U08.AO.02 – Practice with Simulating a Compound Event

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All Things Algebra®

Math 7 Unit 8: Probability & Statistics

This unit includes 59 pages of guided notes, homework assignments, three quizzes, a study guide, and a unit test that cover the topics listed in the description below.

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This unit contains the following topics:

• Outcomes and Events • Theoretical Probability (Simple Events) • Theoretical vs. Experimental Probability • Tree Diagrams • Fundamental Counting Principle • Compound Probability (independent events only) • Populations and Samples • Biased vs. Unbiased Samples • Using Sampling to Predict • Measures of Center: Mean, Median, and Mode • Range • Stem-and-Leaf Plots • Histograms • Box-and-Whisker Plots

This unit does not contain activities.

This is the guided notes, homework assignments, quizzes, study guide, and unit test only.  For suggested activities to go with this unit, check out the ATA Activity Alignment Guides .

This resource is included in the following bundle(s):

Math 7 Curriculum

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This purchase includes a single non-transferable license, meaning it is for one teacher only for personal use in their classroom and can not be passed from one teacher to another.  No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.  A t ransferable license is not available for this resource.

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No part of this resource may be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

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I bought this resource, because our "regular" curriculum doesn't include any probability and statistics in it, and it's part of the standards. In addition, it's a really fun way to end the year for students. My students really enjoy EVERYTHING I purchase from ATA, and this was no exception.

My advanced sections complete 7th grade standards and sometimes need additional practice to meet mastery. This was a great way to provide that to them to ensure they were confident in the content.

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Don't be fooled by "Grade 7" -- these resources are great right up through high school if you have students who wouldn't otherwise see much probability (as is the case for us with some curriculum shuffles). I was able to use this, along with the All Things Algebra Geometry Probability Unit, to mix-and-match a "custom" probability unit that does a really nice job of ramping up from intro level to high school. As always, a worthwhile investment.

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Curriculum  /  Math  /  7th Grade  /  Unit 8: Probability  /  Lesson 8

Probability

Lesson 8 of 9

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Lesson Notes

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Determine the probability of compound events.

Common Core Standards

Core standards.

The core standards covered in this lesson

Statistics and Probability

7.SP.C.8 — Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Determine the sample space for a compound event and use lists, tables, or tree diagrams as needed to organize the sample space.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

A fair six-sided die is rolled twice. What is the theoretical probability that the first number that comes up is greater than or equal to the second number?

Guiding Questions

Student response.

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Rolling Twice , accessed on June 14, 2017, 2:49 p.m., is licensed by Illustrative Mathematics under either the  CC BY 4.0  or  CC BY-NC-SA 4.0 . For further information, contact Illustrative Mathematics .

Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the theoretical probability that Angie and Carlos are seated opposite each other?

Sitting Across from Each Other , accessed on June 14, 2017, 2:40 p.m., is licensed by Illustrative Mathematics under either the  CC BY 4.0  or  CC BY-NC-SA 4.0 . For further information, contact Illustrative Mathematics .

A standard deck of playing cards includes 52 cards, equally divided among 4 suits: hearts, diamonds, clubs, and spades.

You have two standard decks of cards. You draw a card from the first deck, record the suit, and then draw a card from the second deck and record the suit.

a.   What is the probability that you draw a heart and a diamond, in that order?

b.   What is the probability that you draw a heart and a diamond, in any order?

A set of suggested resources or problem types that teachers can turn into a problem set

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Lin plays a game that involves a standard number cube and a spinner with four equal sections numbered 1 through 4. If both the cube and spin result in the same number, Lin gets another turn. Otherwise, play continues with the next player. What is the probability that Lin gets another turn?

Grade 7 Unit 8 Lesson 9 Teacher Version is made available by Open Up Resources  under the  CC BY 4.0  license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed April 5, 2018, 1:13 p.m..

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

• MARS Summative Assessment Tasks for Middle School Memory Game
• Illustrative Mathematics Red, Green, or Blue? — (Note: this is a challenging problem that would be a good problem for students to do in pairs)
• Open Up Resources Grade 7 Unit 8 Practice Problems — Lesson 9

Topic A: Probability Models of Simple Events

Understand the probability of an event happening is a number between 0 and 1, ranging from impossible to certain.

Define probability and sample space. Estimate probabilities from experimental data.

7.SP.C.6 7.SP.C.7

Determine the probability of events.

7.SP.C.7.A 7.SP.C.7.B

Use probability to predict long-run frequencies.

Design and conduct simulations to model real-world situations.

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Topic B: Probability Models of Compound Events

Conduct simulations with multiple events to determine probabilities.

7.SP.C.8 7.SP.C.8.C

List the sample space for compound events using organized lists, tables, or tree diagrams.

Design and conduct simulations to model real-world situations for compound events.

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Statistics and Probability Worksheets

Welcome to the statistics and probability page at Math-Drills.com where there is a 100% chance of learning something! This page includes Statistics worksheets including collecting and organizing data, measures of central tendency (mean, median, mode and range) and probability.

Students spend their lives collecting, organizing, and analyzing data, so why not teach them a few skills to help them on their way. Data management is probably best done on authentic tasks that will engage students in their own learning. They can collect their own data on topics that interest them. For example, have you ever wondered if everyone shares the same taste in music as you? Perhaps a survey, a couple of graphs and a few analysis sentences will give you an idea.

Statistics has applications in many different fields of study. Budding scientists, stock market brokers, marketing geniuses, and many other pursuits will involve managing data on a daily basis. Teaching students critical thinking skills related to analyzing data they are presented will enable them to make crucial and informed decisions throughout their lives.

Probability is a topic in math that crosses over to several other skills such as decimals, percents, multiplication, division, fractions, etc. Probability worksheets will help students to practice all of these skills with a chance of success!

Most Popular Statistics and Probability Worksheets this Week

Mean, Median, Mode and Range Worksheets

Calculating the mean, median, mode and range are staples of the upper elementary math curriculum. Here you will find worksheets for practicing the calculation of mean, median, mode and range. In case you're not familiar with these concepts, here is how to calculate each one. To calculate the mean, add all of the numbers in the set together and divide that sum by the number of numbers in the set. To calculate the median, first arrange the numbers in order, then locate the middle number. In sets where there are an even number of numbers, calculate the mean of the two middle numbers. To calculate the mode, look for numbers that repeat. If there is only one of each number, the set has no mode. If there are doubles of two different numbers and there are more numbers in the set, the set has two modes. If there are triples of three different numbers and there are more numbers in the set, the set has three modes, and so on. The range is calculated by subtracting the least number from the greatest number.

Note that all of the measures of central tendency are included on each page, but you don't need to assign them all if you aren't working on them all. If you're only working on mean, only assign students to calculate the mean.

In order to determine the median, it is necessary to have your numbers sorted. It is also helpful in determining the mode and range. To expedite the process, these first worksheets include the lists of numbers already sorted.

• Calculating Mean, Median, Mode and Range from Sorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Normally, data does not come in a sorted list, so these worksheets are a little more realistic. To find some of the statistics, it will be easier for students to put the numbers in order first.

• Calculating Mean, Median, Mode and Range from Unsorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Collecting and Organizing Data

Teaching students how to collect and organize data enables them to develop skills that will enable them to study topics in statistics with more confidence and deeper understanding.

• Constructing Line Plots from Small Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Smaller Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Smaller Numbers (Small Data Set) Construct Line Plots with Larger Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Larger Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Larger Numbers (Small Data Set)
• Constructing Line Plots from Larger Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided Construct Line Plots with Smaller Numbers and Lines Only Provided Construct Line Plots with Smaller Numbers Construct Line Plots with Larger Numbers and Lines with Ticks Provided Construct Line Plots with Larger Numbers and Lines Only Provided Construct Line Plots with Larger Numbers

Interpreting and Analyzing Data

Answering questions about graphs and other data helps students build critical thinking skills. Standard questions include determining the minimum, maximum, range, count, median, mode, and mean.

• Answering Questions About Stem-and-Leaf Plots Stem-and-Leaf Plots with about 25 data points Stem-and-Leaf Plots with about 50 data points Stem-and-Leaf Plots with about 100 data points
• Answering Questions About Line Plots Line Plots with Smaller Data Sets and Smaller Numbers Line Plots with Smaller Data Sets and Larger Numbers Line Plots with Larger Data Sets and Smaller Numbers Line Plots with Larger Data Sets and Larger Numbers
• Answering Questions About Broken-Line Graphs Answer Questions About Broken-Line Graphs
• Answering Questions About Circle Graphs Circle Graph Questions (Color Version) Circle Graph Questions (Black and White Version) Circle Graphs No Questions (Color Version) Circle Graphs No Questions (Black and White Version)
• Answering Questions About Pictographs Answer Questions About Pictographs

Probability Worksheets

• Calculating Probabilities with Dice Sum of Two Dice Probabilities Sum of Two Dice Probabilities (with table)

Spinners can be used for probability experiments or for theoretical probability. Students should intuitively know that a number that is more common on a spinner will come up more often. Spinning 100 or more times and tallying the results should get them close to the theoretical probability. The more sections there are, the more spins will be needed.

• Calculating Probabilities with Number Spinners Number Spinner Probability (4 Sections) Number Spinner Probability (5 Sections) Number Spinner Probability (6 Sections) Number Spinner Probability (7 Sections) Number Spinner Probability (8 Sections) Number Spinner Probability (9 Sections) Number Spinner Probability (10 Sections) Number Spinner Probability (11 Sections) Number Spinner Probability (12 Sections)

Non-numerical spinners can be used for experimental or theoretical probability. There are basic questions on every version with a couple extra questions on the A and B versions. Teachers and students can make up other questions to ask and conduct experiments or calculate the theoretical probability. Print copies for everyone or display on an interactive white board.

• Probability with Single-Event Spinners Animal Spinner Probability ( 4 Sections) Animal Spinner Probability ( 5 Sections) Animal Spinner Probability ( 10 Sections) Letter Spinner Probability ( 4 Sections) Letter Spinner Probability ( 5 Sections) Letter Spinner Probability ( 10 Sections) Color Spinner Probability ( 4 Sections) Color Spinner Probability ( 5 Sections) Color Spinner Probability ( 10 Sections)
• Probability with Multi-Event Spinners Animal/Letter Combined Spinner Probability ( 4 Sections) Animal/Letter Combined Spinner Probability ( 5 Sections) Animal/Letter Combined Spinner Probability ( 10 Sections) Animal/Letter/Color Combined Spinner Probability ( 4 Sections) Animal/Letter/Color Combined Spinner Probability ( 5 Sections) Animal/Letter/Color Combined Spinner Probability ( 10 Sections)

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Compound Probability

Compound probability is the probability of two or more independent events occurring together. Compound probability can be calculated for two types of compound events, namely, mutually exclusive and mutually inclusive compound events. The formulas to calculate the compound probability for both types of events are different.

Compound probability is a concept that is widely used in the finance industry to assess risks and assign premiums to various policies. In this article, we will learn more about compound probability, its formulas, how to determine it as well as see various associated examples.

What is Compound Probability?

The compound probability of compound events (mutually inclusive or mutually exclusive) can be defined as the likelihood of occurrence of two or more independent events together. An independent event is one whose outcome is not affected by the outcome of other events. A mutually inclusive event is a situation where one event cannot occur with the other while a mutually exclusive event is when both events cannot take place at the same time. The compound probability will always lie between 0 and 1.

Compound Probability Formulas

There are two formulas to calculate the compound probability depending on the type of events that occur. In general, to find the compound probability, the probability of the first event is multiplied by the probability of the second event and so on. The compound probability formulas are given below:

Mutually Exclusive Events Compound Probability

• P(A or B) = P(A) + P(B)

Using set theory this formula is given as,

• P(A ∪ B) = P(A) + P(B)

Mutually Inclusive Events Compound Probability

• P(A or B) = P(A) + P(B) - P(A and B)
• P(A ∪ B) = P(A) + P(B) - P(A ⋂ B)

where A and B are two independent events, and P(A and B) = P(A) x P(B)

Compound Probability Example

Suppose a coin is tossed. The outcome of getting heads will be a simple event with a probability of 1 / 2. However, if the coin is tossed twice then the outcome of getting two heads will be a compound event. The compound probability of this event can be calculated as (1 / 2) x (1 / 2) = 1 / 4 or 0.25. This is an example of compound probability.

How to Find Compound Probability?

The steps to apply the compound formulas can be understood with the help of an example. Suppose the probability of Ryan failing an exam is 0.3 and the probability of Berta failing is 0.2. Then to find the compound probability of Ryan or Berta failing, the steps are as follows:

• Determine if the compound event is mutually exclusive or inclusive. This is an example of a mutually inclusive event.
• List the given probabilities. P(R) = 0.3 and P(B) = 0.2.
• Determine the correct compound probability formula. This is P(A or B) = P(A) + P(B) - P(A and B) for the given example
• Find P(A and B) which is given by P(A) x P(B). Thus, 0.2 x 0.3 = 0.6.
• Plug the values into the formula to get the result. Thus, the compound probability for the example is 0.44

Related Articles:

• Probability Rules
• Events in Probability
• Exhaustive Events
• Dependent Events
• Mathematical Induction

Important Notes on Compound Probability

• Compound probability is the likelihood of occurrence of two independent compound events together.
• Compound probability can be calculated for mutually exclusive and mutually inclusive compound events.
• P(A or B) = P(A) + P(B) and P(A or B) = P(A) + P(B) - P(A and B) are the compound probability formulas.

Examples on Compound Probability

Example 1: There are 40 girls and 30 boys in a class. 10 girls and 20 boys like tennis while the rest like swimming. If a student is selected at random then what is the probability that it will be a boy or a girl.

Solution: If a student is selected it can only be a girl or a boy. Thus, the probability that the selected student will be a girl or a boy is 1.

Answer: P(Boy or Girl) = 1

Example 2: If a dice is rolled then find the compound probability that either a 2 or 3 will be obtained.

Solution: P(2) = 1 / 6

P(3) = 1 / 6

As this is an example of a mutually exclusive event thus, the compound probability formula used is

P(2 or 3) = (1 / 6) + (1 / 6)

Answer: P(2 or 3) = 1 / 3

Example 3: Find the compound probability of selecting 5 or a black card from a deck.

Solution: Total number of cards in a deck = 52

Number of cards in each suit = 13

P(Black card) = 26 / 52

Total number of 5s in a deck = 4

P(5) = 4 / 52

Number of 5s in black cards = 2

P(Black card and 5) = 2 / 52

This is a mutually inclusive event thus, the compound probability formula is

P(Black card or 5) = P(Black card) + P(5) - P(Black card and 5)

Answer: P(Black card or 5) = 7 / 13

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FAQs on Compound Probability

What is the meaning of compound probability.

Compound probability, in probability and statistics , is the probability that describes the chance that two or more independent events will occur together. It is determined by multiplying the probabilities of the occurring events.

What is the Formula for Compound Probability?

There are two formulas available for calculating the compound probability. These are given as follows:

What is the Formula for Compound Probability in Set Theory?

The compound theory formulas expressed using set operations are given as follows:

What are the Types of Events Used in Compound Probability?

There are two types of events used in compound probability. These are mutually exclusive and mutually inclusive compound events.

Can Compound Probability be Greater Than 1?

The compound probability value will always lie between 0 and 1. 0 indicates that the event will never occur and 1 denotes that the event will definitely take place.

What is the Difference between Simple and Compound Probability?

Simple probability is used to give the likelihood that one event will take place. On the other hand, compound probability gives the probability of occurrence of more than one separate event.

How to Calculate Compound Probability?

The steps to calculate the compound probability are as follows:

• Determine if the event is mutually inclusive or mutually exclusive.
• Apply the corresponding formula.

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Unit 8: Statistics And Probability

Students will master the process of collecting, organizing and representing data and also understand how information can be used and displayed to make an argument.  This unit will also focus on developing your student’s ability to sample and experiment, analyze data and find patterns in that data to better understand the world around us.  Students will also explore basic probability and chance to make simple predictions of future events.

Theorems Your Student Will Discover:

Probability

How to determine the probability of a single event

How to determine the probability of compound events

How to determine the probability of conditional events

How to determine the number of outcomes of a permutation

How to determine the number of outcomes of a combination

Data Analysis

How to find the mean of a set of data

How to find a data element given the mean

How to find missing elements of a set of data given either the mean, median, mode, range or a combination of them

Displaying Data

How to create a box and whisker plot given a set of data

How to create a histogram plot given a set of data

How to create a pie chart given a set of data

How to create a scatter plot given a set of data

How to identify correlation given a scatter plot or set of data

How to draw a line of best fit

Pre-Algebra

How to write a linear equation given a set of data

How to write a linear equation given the graph of a set of data

How to draw the line of best fit given a linear equation

How to solve a system of linear equations using a graph

Definitions:

Sample Size

Variability

Simple Random Sample

Stratified Sampling

Cluster Sampling

Systematic Sampling

Multistage Sampling

Theoretical Probability

Experimental Probability

Independent Event

Dependent Event

Conditional Probability

Permutation

Combination

Box And Whisker Plot

Scatter Plot

Correlation

Line of Best Fit

System Of Equations

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