# MATH STUDENT BOOK. 7th Grade Unit 6

Size: px
Start display at page:

Transcription

1 MATH STUDENT BOOK 7th Grade Unit 6

2 Unit 6 Probability and Graphing Math 706 Probability and Graphing Introduction 3 1. Probability 5 Theoretical Probability 5 Experimental Probability 13 Sample Space 20 Independent and Dependent Events 29 Self Test 1: Probability Functions 39 Graphing Ordered Pairs 39 Graphing Linear Equations 50 Slope 59 Direct Variation 68 Self Test 2: Functions Review 83 LIFEPAC Test is located in the center of the booklet. Please remove before starting the unit. Section 1 1

3 Probability and Graphing Unit 6 Author: Glynlyon Staff Editors: Alan Christopherson, M.S. Michelle Chittam Westover Studios Design Team: Phillip Pettet, Creative Lead Teresa Davis, DTP Lead Nick Castro Andi Graham Jerry Wingo 804 N. 2nd Ave. E. Rock Rapids, IA MMXIV by Alpha Omega Publications, a division of Glynlyon, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc. All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/ or service marks other than their own and their affiliates, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own. Some clip art images used in this curriculum are from Corel Corporation, 1600 Carling Avenue, Ottawa, Ontario, Canada K1Z 8R7. These images are specifically for viewing purposes only, to enhance the presentation of this educational material. Any duplication, resyndication, or redistribution for any other purpose is strictly prohibited. Other images in this unit are 2009 JupiterImages Corporation 2 Section 1

4 Unit 6 Probability and Graphing Probability and Graphing Introduction In this unit, students will be introduced to basic probability. They will determine theoretical and experimental probability and learn that experimental probability approaches theoretical probability as the number of trials increases. Students will determine the probability for compound events and find sample space using a tree diagram and a table. Students will learn about the counting principle and apply it to finding the probability of compound events. They will also learn the difference between independent and dependent events. Students will be introduced to the coordinate plane and use it to graph linear functions. They will plot ordered pairs and find the location of points in the coordinate plane. Students will graph linear equations and determine the slope of a line using the slope formula. They will also learn about direct variation functions and their characteristics. Objectives Read these objectives. The objectives tell you what you will be able to do when you have successfully completed this LIFEPAC. When you have finished this LIFEPAC, you should be able to: z Determine the theoretical and experimental probability of an event. z Determine the sample space for an experiment. z Determine if events are independent or dependent. z Determine the probability of independent and dependent events. z Plot ordered pairs on a rectangular coordinate system. z Use a table to graph a linear equation. z Determine the slope of a linear function, including direct variation. z Determine if a function is a direct variation. z Graph direct variations. Section 1 3

5 Unit 6 Probability and Graphing 1. Probability Theoretical Probability How likely is it that Ondi will win the game? What are her chances, and how can you figure that out? In this lesson, you will learn how to find the likelihood that events will occur. The measure of this likelihood is called probability. Objectives Determine the theoretical probability of an event. Vocabulary complementary events two disjoint events of which one or the other must occur disjoint events events that have no outcomes in common event a specific outcome or group of outcomes experiment any activity that has two or more outcomes favorable outcome outcome for a specific event outcome any possible result of an experiment probability the measure of the likelihood of an event theoretical probability a ratio representing the likelihood of an event In the area of mathematics known as probability, the carnival game that Ondi wanted to play is called an experiment. There are 20 possible outcomes, or results of the experiment because the spinner could stop on any number. The event, or specific outcome, that Ondi would need to win is any multiple of 3 from 1 and 20. The outcomes for this event are called favorable outcomes. Section 1 5

6 Probability and Graphing Unit 6 Probability is a measure of how likely an event is to occur. If all outcomes are equally likely, the probability (P) of the event is expressed as a ratio: For Ondi, the event is spinning a multiple of 3 on the wheel. Take a look at the probability of Ondi winning the carnival game. Example: What is the probability of spinning a multiple of 3 on a spinner with 20 equally spaced sections numbered from 1 to 20? Solution: You need to find the number of favorable outcomes compared to the total number of outcomes. You know there are 20 spaces on the spinner, so the total number of outcomes is 20. To find the number of favorable outcomes, look at the multiples of 3 from 1 to 20: 3, 6, 9, 12, 15, 18 There are 6 multiples of 3, so there are 6 favorable outcomes. Shading in the multiples of 3 on the wheel makes this easier to see. Reminder! Percents, decimals, and fractions can each express the same ratio: = = 25% = 0.25 Now compare the number of favorable outcomes to the total number of outcomes: P(multiple of 3) = Since probability is a ratio, it can be written as a fraction, decimal, or percent. When you express the probability of an event as a ratio, it is called the theoretical probability. Reminder! To change a fraction to a percent, rewrite it with a denominator of 100. To change a percent to a decimal, move the decimal point two places to the left. = = = 30% 30% = 0.3 Divide by a common factor of 2. Multiply by 10 to get a denominator of 100. Convert the fraction to a percent. Move the decimal point two places to the left. 6 Section 1

7 Unit 6 Probability and Graphing So there is a, 30%, or 0.3 chance of spinning a multiple of 3 on the wheel. Probability will always be a number from 0 to 1. The closer the probability is to 1, the more likely it is that the event will occur. You can see this relationship on a number line. Events that have less than a 50% probability are less likely to occur. Events that have more than a 50% probability are more likely to occur. As Carlton said, it is unlikely that Ondi would win the game. She has well under a 50% chance of winning. You can also describe everyday events in terms of likelihood. For example, it is very unlikely that it will snow on a warm summer day. Or suppose you ve attended school 48 out of the last 50 school days. Based on your previous attendance, it is very likely that you will be at school on the next school day. Take a look at a couple of examples using the carnival spinning wheel. For each event, look at the number of favorable outcomes compared to the number of total outcomes. What is the probability that you would spin the number 30? There are 20 total outcomes, because there are 20 sections on the wheel. However, you can see from looking at the wheel that there is no space labeled 30, so there are 0 favorable outcomes. You can express this probability using a ratio: P(30) = Make note! In probability, parentheses do not indicate multiplication. The contents of the parentheses are the event. You are not multiplying P by 30. So the probability is 0 out of 20, or 0%. In other words, the outcome is impossible. What is the probability that you would spin a number less than 21? Again, there are 20 total outcomes, because there are 20 sections on the wheel. There are 20 favorable outcomes because all of the outcomes are less than 21. You can express this probability using a ratio: Section 1 7

8 Probability and Graphing Unit 6 P(< 21) = So the probability is 20 out of 20, or 1, or 100%. In other words, the outcome is certain. Here s another example. Example: There are 2 blue marbles, 1 red marble, and 9 green marbles in a bag. What is the probability of drawing a green marble from the bag? Solution: Find the number of favorable outcomes and the total number of outcomes and compare them to find the probability of the event. There are 9 green marbles, so there are 9 favorable outcomes. To find the total number of outcomes, you need to find out how many marbles are in the bag: 2 blue + 1 red + 9 green = 12 marbles Since there are 12 marbles in the bag, there are 12 total outcomes. Now compare the outcomes: P(green) = Keep in mind! Any proportion can be solved by cross multiplying: = 300 = 4x = x 75 = x You can simplify the fraction and change it to a percent or a decimal. = = 75% = 0.75 Divide by a common factor of 3. Multiply by 25 to get a denominator of 100. Move the decimal point two places to the left. So there is a, 0.75, or 75% chance of drawing a green marble from the bag. When you have two events of which one or the other must occur, the events are called complementary events, and their probabilities will always add up to 1: P(event) + P(not event) = 1 Try an example involving complementary events. Example: If you roll a regular 6-sided number cube, what is the probability that you will roll a 4? What is the probability that you won t roll a 4? Solution: Compare the number of favorable outcomes to the total number of outcomes for each experiment. Write the probability as a fraction this time. 8 Section 1

9 Unit 6 Probability and Graphing There is only one favorable outcome for each of the 6 numbers on the cube, so there is one favorable outcome for rolling a 4. There are 6 sides to the number cube, so there are a total of 6 outcomes. Example: If you spin the carnival spinning wheel, what is the probability that you will spin a multiple of 5 or a multiple of 7? P(4) = The favorable outcomes for not rolling a 4 are 1, 2, 3, 5, and 6. So there are 5 favorable outcomes out of 6 total outcomes. P(not 4) = Notice that the probability of rolling a 4 and the probability of not rolling a 4 add up to 1: P(4) + P(not 4) = + = 1 They add up to 1 because both events together account for all of the outcomes. You could say that all rolls of the number cube are either 4 or not 4. Events that have no outcomes in common are called disjoint events, and the probability that either event will occur is the sum of the probabilities of the events: P(event 1 or event 2) = P(event 1) + P(event 2) Try an example involving disjoint events. Solution: Compare the number of favorable outcomes to the total outcomes for each event. This will give you the probability for each event. If there are no outcomes in common, you can add the probabilities of the events. The favorable outcomes for a multiple of 5 are 5, 10, 15, and 20. So there are 4 favorable outcomes. You know there are 20 total outcomes because there are 20 spaces on the wheel. P(multiple of 5) = The favorable outcomes for a multiple of 7 are 7 and 14. So there are 2 favorable outcomes out of 20 total outcomes. Section 1 9

10 Probability and Graphing Unit 6 P(multiple of 7) = If the wheel is colored, you can see the favorable outcomes more easily. yellow: multiples of 5 orange: multiples of 7 There are no outcomes in common, so you can add the probabilities. P(event 1 or event 2) = P(event 1) + P(event 2) P(multiple of 5 or multiple of 7) = P(multiple of 5) + P(multiple of 7) P(multiple of 5 or multiple of 7) = + P(multiple of 5 or multiple of 7) = This was the same probability as the game Ondi wanted to play, and you found that 6 out of 20 was 30%. So there is a 30% chance of spinning a multiple of 5 or 7. Example: A side game at the fair requires the game operator to guess the month of the guest s birth within 2 months. If the game operator is off by more than two months, the guest wins a prize. What is the probability that the game operator will randomly guess a person s birth month within two months of the correct month? Solution: There are 12 possible months to choose from, so there are 12 possible outcomes. Of these possible outcomes, the game operator must either guess the correct month, or one of the two months on either side of the correct month. For example, if the guest was born in July, the game operator could guess July (the correct month), August, September (the 2 months after July), June, or May (the 2 months before July). This allows 5 possible favorable outcomes. Compare the number of favorable outcomes with the number of possible outcomes and form a ratio. favorable outcomes possible outcomes = 5 12 P( birth month within 2 months ) 2 or 41.6% or = Section 1

11 Unit 6 Probability and Graphing Let s Review Before going on to the practice problems, make sure you understand the main points of this lesson: Theoretical probability is expressed as a ratio and can be written as a fraction, decimal, or percent. To find the theoretical probability of an event, compare the number of favorable outcomes to the total number of outcomes: Complete the following activities. 1.1 Select all that apply. If there are 8 chocolate chip cookies out of 20 total cookies in a jar, what is the probability that you will randomly choose a chocolate chip cookie? 40% Select all that apply. In a carnival game, there is a 45% probability of winning a prize. Which of the following is true? The probability that you won t win The probability that you won t win is. is The probability that you will win is 4.5. The probability that you will win is. 1.3 In a raffle, Scott buys 10 tickets and his friend Tom buys 6 tickets. If there are 80 tickets sold, what is the probability that Scott or Tom will win? 1.4 A jar contains 100 coins. If it is very unlikely that you will randomly choose a quarter out of the jar, how many quarters could be in the jar? At a school, there are 526 students and 263 are girls. About how likely is it that a randomly chosen student will be a boy? unlikely equally as likely as unlikely somewhat likely very likely Section 1 11

12 Probability and Graphing Unit What is the probability of rolling a 2 or not rolling a 2 using a regular 6-sided number cube? 33.3% 100% 1.7 Chris has 2 pairs of black socks, 4 pairs of red socks, and 18 pairs of white socks in a dresser drawer. If he reaches in his drawer without looking, what is the probability that he will choose a pair of white socks? 75% 33.3% 25% 50% 1.8 There are 6 red marbles, 4 blue marbles, and 15 green marbles in a jar. If you reach in and randomly draw one, what is the probability that you will choose a red marble? 66.7% 40% 30% 24% 1.9 There are 12 boys and 13 girls in a class. If the teacher randomly chooses a student s name out of a hat, what is the probability it will be a girl? 48% 50% 52% 92% 1.10 You are one of 50 people with an entry into a random drawing for a new bicycle. What is the probability that you will win the drawing? 1.11 You must roll an even number on a standard 6-sided game die to win the game. What is the probability that you will win the game on your next roll? 1.12 What is the probability of a football player correctly guessing whether the coin toss will be heads or tails? 1.13 What is the probability of rolling either an even number or a 5 on a standard 6-side game die? 1.14 A deck of cards has 52 cards (13 cards in each of 4 suits: clubs, diamonds, spades, and hearts). What is the probability of drawing a card with a diamond on it? 12 Section 1

13 Probability and Graphing Unit 6 Self Test 1: Probability Complete the following activities (5 points, each numbered activity) Suppose you are asked to pick 3 numbers from 1 to 20 to win a prize. What is the probability that one of the numbers you will pick is the winning number? 5% 10% 15% 20% 1.02 At a carnival game, there is a 38% probability of winning a prize. What is the probability of not winning a prize? 38% 50% 62% 76% 1.03 Alice and Finn roll two number cubes. Which of the following rules will make the game fair? Alice wins if a total of 5 is rolled. Finn wins if a total of 9 is rolled. Alice wins if a total of 7 is rolled. Finn wins if a total of 8 is rolled. Alice wins if a total of 3 is rolled. Finn wins if a total of 10 is rolled. Alice wins if a total of 4 is rolled. Finn wins if a total of 11 is rolled You have 2 spreads, 5 meats, and 2 kinds of bread. How many different sandwiches can you make using one of each type of ingredient? There are 6 red marbles, 8 blue marbles, and 11 green marbles in a bag. What is the probability that you will randomly draw either a red or a blue marble? 24% 56% 32% 10% 1.06 What is the experimental probability of drawing a red marble, given the following results? Marble Color Blue Green Red Times Drawn A coin is flipped 40 times, and it lands on heads 16 times. Based on the experimental probability, how many heads would you predict for 200 flips of the coin? Section 1

14 Unit 6 Probability and Graphing 1.08 Select all that apply. A spinner is divided into 4 equal sections. Which of the following are true? The spinner will land on each section of the spinner an equal number of times. The theoretical probability is 25% for each section. If the spinner is spun 64 times, you would predict it to land on each section 16 times. The experimental probability is for each section Select all that apply. There are 3 red marbles, 5 green marbles, and 2 blue marbles in a bag. Which of the following are true? The probability of randomly drawing either a red marble or a green marble is 80%. The probability of randomly drawing a red marble and then a green marble is. The probability of not drawing a blue marble is 20%. The probability of drawing a green marble is the same as the probability of drawing either a red or a blue marble Select all that apply. A coin is flipped and a number cube is rolled. Which of the following are true? Each result is equally likely. The sample space has 12 different outcomes. The sample space has 8 different outcomes. Heads and an even number are very likely Three coins are flipped. What is the probability that there will be at least two tails? Suppose there are 21 students in your class. If the teacher draws 2 names at random, what is the probability that you and your best friend will be chosen? Which of the following are dependent events? rolling a number cube and then flipping a coin spinning a spinner and then rolling a number cube drawing a marble from a bag, not replacing it, and then drawing a second marble choosing a number from a hat, replacing it, and then choosing another number Section 1 37

15 Probability and Graphing Unit What is the probability of rolling an odd number and spinning B, given the sample space below? A A1 A2 A3 A4 A5 A6 B B1 B2 B3 B4 B5 B6 C C1 C2 C3 C4 C5 C6 D D1 D2 D3 D4 D5 D A number cube is rolled and a coin is flipped. Predict how many times you would get heads and a number less than 3 in 240 trials What is the probability of rolling doubles on a pair of standard 6-sided dice? What is the probability of rolling doubles three times in a row on a pair of standard 6-sided dice? You have 8 tickets out of the 150 tickets in a drawing. What is the probability that one of your tickets will be drawn first? A baseball player s batting average is 0.333, which means he gets a hit 33% of the time, or 1 3 of the time. Based on this information, how many hits would you expect the player to have in a series if he has 12 at-bats in the series? How many meal combinations are possible that contain one appetizer, one entrée, and one dessert from a menu with 4 appetizers, 5 entrées, and 3 desserts? SCORE TEACHER initials date 38 Section 1

16 MAT0706 May 14 Printing ISBN N. 2nd Ave. E. Rock Rapids, IA

### MATH STUDENT BOOK. 8th Grade Unit 10

MATH STUDENT BOOK 8th Grade Unit 10 Math 810 Probability Introduction 3 1. Outcomes 5 Tree Diagrams and the Counting Principle 5 Permutations 12 Combinations 17 Mixed Review of Outcomes 22 SELF TEST 1:

### MATH STUDENT BOOK. 6th Grade Unit 7

MATH STUDENT BOOK 6th Grade Unit 7 Unit 7 Probability and Geometry MATH 607 Probability and Geometry. PROBABILITY 5 INTRODUCTION TO PROBABILITY 6 COMPLEMENTARY EVENTS SAMPLE SPACE 7 PROJECT: THEORETICAL

### When a number cube is rolled once, the possible numbers that could show face up are

C3 Chapter 12 Understanding Probability Essential question: How can you describe the likelihood of an event? Example 1 Likelihood of an Event When a number cube is rolled once, the possible numbers that

### Unit 7 Central Tendency and Probability

Name: Block: 7.1 Central Tendency 7.2 Introduction to Probability 7.3 Independent Events 7.4 Dependent Events 7.1 Central Tendency A central tendency is a central or value in a data set. We will look at

### NAME DATE PERIOD. Study Guide and Intervention

9-1 Section Title The probability of a simple event is a ratio that compares the number of favorable outcomes to the number of possible outcomes. Outcomes occur at random if each outcome occurs by chance.

### Grade 8 Math Assignment: Probability

Grade 8 Math Assignment: Probability Part 1: Rock, Paper, Scissors - The Study of Chance Purpose An introduction of the basic information on probability and statistics Materials: Two sets of hands Paper

### 1. Theoretical probability is what should happen (based on math), while probability is what actually happens.

Name: Date: / / QUIZ DAY! Fill-in-the-Blanks: 1. Theoretical probability is what should happen (based on math), while probability is what actually happens. 2. As the number of trials increase, the experimental

### Name: Class: Date: ID: A

Class: Date: Chapter 0 review. A lunch menu consists of different kinds of sandwiches, different kinds of soup, and 6 different drinks. How many choices are there for ordering a sandwich, a bowl of soup,

### CCM6+7+ Unit 11 ~ Page 1. Name Teacher: Townsend ESTIMATED ASSESSMENT DATES:

CCM6+7+ Unit 11 ~ Page 1 CCM6+7+ UNIT 11 PROBABILITY Name Teacher: Townsend ESTIMATED ASSESSMENT DATES: Unit 11 Vocabulary List 2 Simple Event Probability 3-7 Expected Outcomes Making Predictions 8-9 Theoretical

### Probability of Independent and Dependent Events

706 Practice A Probability of In and ependent Events ecide whether each set of events is or. Explain your answer.. A student spins a spinner and rolls a number cube.. A student picks a raffle ticket from

### Math 7 Notes - Unit 7B (Chapter 11) Probability

Math 7 Notes - Unit 7B (Chapter 11) Probability Probability Syllabus Objective: (7.2)The student will determine the theoretical probability of an event. Syllabus Objective: (7.4)The student will compare

### Fair Game Review. Chapter 9. Simplify the fraction

Name Date Chapter 9 Simplify the fraction. 1. 10 12 Fair Game Review 2. 36 72 3. 14 28 4. 18 26 5. 32 48 6. 65 91 7. There are 90 students involved in the mentoring program. Of these students, 60 are girls.

### Lesson 16.1 Assignment

Lesson 16.1 Assignment Name Date Rolling, Rolling, Rolling... Defining and Representing Probability 1. Rasheed is getting dressed in the dark. He reaches into his sock drawer to get a pair of socks. He

### Making Predictions with Theoretical Probability

? LESSON 6.3 Making Predictions with Theoretical Probability ESSENTIAL QUESTION Proportionality 7.6.H Solve problems using qualitative and quantitative predictions and comparisons from simple experiments.

### Find the probability of an event by using the definition of probability

LESSON 10-1 Probability Lesson Objectives Find the probability of an event by using the definition of probability Vocabulary experiment (p. 522) trial (p. 522) outcome (p. 522) sample space (p. 522) event

### Most of the time we deal with theoretical probability. Experimental probability uses actual data that has been collected.

AFM Unit 7 Day 3 Notes Theoretical vs. Experimental Probability Name Date Definitions: Experiment: process that gives a definite result Outcomes: results Sample space: set of all possible outcomes Event:

### 4.1 Sample Spaces and Events

4.1 Sample Spaces and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment is called an

### COMPOUND EVENTS. Judo Math Inc.

COMPOUND EVENTS Judo Math Inc. 7 th grade Statistics Discipline: Black Belt Training Order of Mastery: Compound Events 1. What are compound events? 2. Using organized Lists (7SP8) 3. Using tables (7SP8)

### Making Predictions with Theoretical Probability. ESSENTIAL QUESTION How do you make predictions using theoretical probability?

L E S S O N 13.3 Making Predictions with Theoretical Probability 7.SP.3.6 predict the approximate relative frequency given the probability. Also 7.SP.3.7a ESSENTIAL QUESTION How do you make predictions

### Essential Question How can you list the possible outcomes in the sample space of an experiment?

. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G..B Sample Spaces and Probability Essential Question How can you list the possible outcomes in the sample space of an experiment? The sample space of an experiment

### TEKSING TOWARD STAAR MATHEMATICS GRADE 7. Projection Masters

TEKSING TOWARD STAAR MATHEMATICS GRADE 7 Projection Masters Six Weeks 1 Lesson 1 STAAR Category 1 Grade 7 Mathematics TEKS 7.2A Understanding Rational Numbers A group of items or numbers is called a set.

### UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet

Name Period Date UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet 20.1 Solving Proportions 1 Add, subtract, multiply, and divide rational numbers. Use rates and proportions to solve problems.

### Key Concepts. Theoretical Probability. Terminology. Lesson 11-1

Key Concepts Theoretical Probability Lesson - Objective Teach students the terminology used in probability theory, and how to make calculations pertaining to experiments where all outcomes are equally

### Section Theoretical and Experimental Probability...Wks 3

Name: Class: Date: Section 6.8......Theoretical and Experimental Probability...Wks 3. Eight balls numbered from to 8 are placed in a basket. One ball is selected at random. Find the probability that it

### Theoretical or Experimental Probability? Are the following situations examples of theoretical or experimental probability?

Name:Date:_/_/ Theoretical or Experimental Probability? Are the following situations examples of theoretical or experimental probability? 1. Finding the probability that Jeffrey will get an odd number

### MATH STUDENT BOOK. 6th Grade Unit 4

MATH STUDENT BOOK th Grade Unit 4 Unit 4 Fractions MATH 04 Fractions 1. FACTORS AND FRACTIONS DIVISIBILITY AND PRIME FACTORIZATION GREATEST COMMON FACTOR 10 FRACTIONS 1 EQUIVALENT FRACTIONS 0 SELF TEST

### Chapter 10 Practice Test Probability

Name: Class: Date: ID: A Chapter 0 Practice Test Probability Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the likelihood of the event given its

### Instructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include your name and student ID.

Math 3201 Unit 3 Probability Test 1 Unit Test Name: Part 1 Selected Response: Instructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include

### Foundations to Algebra In Class: Investigating Probability

Foundations to Algebra In Class: Investigating Probability Name Date How can I use probability to make predictions? Have you ever tried to predict which football team will win a big game? If so, you probably

### Name: Class: Date: 6. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is 11

Class: Date: Sample Mastery # Multiple Choice Identify the choice that best completes the statement or answers the question.. One repetition of an experiment is known as a(n) random variable expected value

### Lesson Lesson 3.7 ~ Theoretical Probability

Theoretical Probability Lesson.7 EXPLORE! sum of two number cubes Step : Copy and complete the chart below. It shows the possible outcomes of one number cube across the top, and a second down the left

### MATH STUDENT BOOK. 6th Grade Unit 6

MATH STUDENT BOOK 6th Grade Unit 6 Unit 6 Ratio, Proportion, and Percent MATH 606 Ratio, Proportion, and Percent INTRODUCTION 3 1. RATIOS 5 RATIOS 6 GEOMETRY: CIRCUMFERENCE 11 RATES 16 SELF TEST 1: RATIOS

### Review. Natural Numbers: Whole Numbers: Integers: Rational Numbers: Outline Sec Comparing Rational Numbers

FOUNDATIONS Outline Sec. 3-1 Gallo Name: Date: Review Natural Numbers: Whole Numbers: Integers: Rational Numbers: Comparing Rational Numbers Fractions: A way of representing a division of a whole into

### Basic Probability Ideas. Experiment - a situation involving chance or probability that leads to results called outcomes.

Basic Probability Ideas Experiment - a situation involving chance or probability that leads to results called outcomes. Random Experiment the process of observing the outcome of a chance event Simulation

### This unit will help you work out probability and use experimental probability and frequency trees. Key points

Get started Probability This unit will help you work out probability and use experimental probability and frequency trees. AO Fluency check There are 0 marbles in a bag. 9 of the marbles are red, 7 are

### A. 15 B. 24 C. 45 D. 54

A spinner is divided into 8 equal sections. Lara spins the spinner 120 times. It lands on purple 30 times. How many more times does Lara need to spin the spinner and have it land on purple for the relative

### Probability. The MEnTe Program Math Enrichment through Technology. Title V East Los Angeles College

Probability The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College 2003 East Los Angeles College. All rights reserved. Topics Introduction Empirical Probability Theoretical

### Lesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes

Lesson : Calculating Probabilities for Chance Experiments with Equally Likely Outcomes Classwork Example : heoretical Probability In a previous lesson, you saw that to find an estimate of the probability

### Name Date Class. 2. dime. 3. nickel. 6. randomly drawing 1 of the 4 S s from a bag of 100 Scrabble tiles

Name Date Class Practice A Tina has 3 quarters, 1 dime, and 6 nickels in her pocket. Find the probability of randomly drawing each of the following coins. Write your answer as a fraction, as a decimal,

### Common Core Math Tutorial and Practice

Common Core Math Tutorial and Practice TABLE OF CONTENTS Chapter One Number and Numerical Operations Number Sense...4 Ratios, Proportions, and Percents...12 Comparing and Ordering...19 Equivalent Numbers,

### Date. Probability. Chapter

Date Probability Contests, lotteries, and games offer the chance to win just about anything. You can win a cup of coffee. Even better, you can win cars, houses, vacations, or millions of dollars. Games

### MATH STUDENT BOOK. 6th Grade Unit 1

MATH STUDENT BOOK 6th Grade Unit 1 Unit 1 Whole Numbers and Algebra MATH 601 Whole Numbers and Algebra INTRODUCTION 3 1. WHOLE NUMBERS AND THEIR PROPERTIES 5 ROUNDING AND ESTIMATION 7 WHOLE NUMBER OPERATIONS

### Lesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes

NYS COMMON CORE MAEMAICS CURRICULUM 7 : Calculating Probabilities for Chance Experiments with Equally Likely Classwork Examples: heoretical Probability In a previous lesson, you saw that to find an estimate

### Part 1: I can express probability as a fraction, decimal, and percent

Name: Pattern: Part 1: I can express probability as a fraction, decimal, and percent For #1 to #4, state the probability of each outcome. Write each answer as a) a fraction b) a decimal c) a percent Example:

### Section 7.1 Experiments, Sample Spaces, and Events

Section 7.1 Experiments, Sample Spaces, and Events Experiments An experiment is an activity with observable results. 1. Which of the follow are experiments? (a) Going into a room and turning on a light.

### MAT104: Fundamentals of Mathematics II Counting Techniques Class Exercises Solutions

MAT104: Fundamentals of Mathematics II Counting Techniques Class Exercises Solutions 1. Appetizers: Salads: Entrées: Desserts: 2. Letters: (A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U,

### Now let s figure the probability that Angelina picked a green marble if Marc did not replace his marble.

Find the probability of an event with or without replacement : The probability of an outcome of an event is the ratio of the number of ways that outcome can occur to the total number of different possible

### Math 1313 Section 6.2 Definition of Probability

Math 1313 Section 6.2 Definition of Probability Probability is a measure of the likelihood that an event occurs. For example, if there is a 20% chance of rain tomorrow, that means that the probability

### Lesson 1: Chance Experiments

Student Outcomes Students understand that a probability is a number between and that represents the likelihood that an event will occur. Students interpret a probability as the proportion of the time that

### Lesson 15.5: Independent and Dependent Events

Lesson 15.5: Independent and Dependent Events Sep 26 10:07 PM 1 Work with a partner. You have three marbles in a bag. There are two green marbles and one purple marble. Randomly draw a marble from the

### Independent Events B R Y

. Independent Events Lesson Objectives Understand independent events. Use the multiplication rule and the addition rule of probability to solve problems with independent events. Vocabulary independent

### Chance and Probability

G Student Book Name Series G Contents Topic Chance and probability (pp. ) probability scale using samples to predict probability tree diagrams chance experiments using tables location, location apply lucky

### Algebra I Notes Unit One: Real Number System

Syllabus Objectives: 1.1 The student will organize statistical data through the use of matrices (with and without technology). 1.2 The student will perform addition, subtraction, and scalar multiplication

### Probability. Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible

Probability Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible Impossible In summer, it doesn t rain much in Cape Town, so on a chosen

### What Do You Expect? Concepts

Important Concepts What Do You Expect? Concepts Examples Probability A number from 0 to 1 that describes the likelihood that an event will occur. Theoretical Probability A probability obtained by analyzing

### A 20% B 25% C 50% D 80% 2. Which spinner has a greater likelihood of landing on 5 rather than 3?

1. At a middle school, 1 of the students have a cell phone. If a student is chosen at 5 random, what is the probability the student does not have a cell phone? A 20% B 25% C 50% D 80% 2. Which spinner

### Probability: introduction

May 6, 2009 Probability: introduction page 1 Probability: introduction Probability is the part of mathematics that deals with the chance or the likelihood that things will happen The probability of an

### Use this information to answer the following questions.

1 Lisa drew a token out of the bag, recorded the result, and then put the token back into the bag. She did this 30 times and recorded the results in a bar graph. Use this information to answer the following

### 2. A bubble-gum machine contains 25 gumballs. There are 12 green, 6 purple, 2 orange, and 5 yellow gumballs.

A C E Applications Connections Extensions Applications. A bucket contains one green block, one red block, and two yellow blocks. You choose one block from the bucket. a. Find the theoretical probability

### Unit 11 Probability. Round 1 Round 2 Round 3 Round 4

Study Notes 11.1 Intro to Probability Unit 11 Probability Many events can t be predicted with total certainty. The best thing we can do is say how likely they are to happen, using the idea of probability.

### Order the fractions from least to greatest. Use Benchmark Fractions to help you. First try to decide which is greater than ½ and which is less than ½

Outcome G Order the fractions from least to greatest 4 1 7 4 5 3 9 5 8 5 7 10 Use Benchmark Fractions to help you. First try to decide which is greater than ½ and which is less than ½ Likelihood Certain

### Probability Essential Math 12 Mr. Morin

Probability Essential Math 12 Mr. Morin Name: Slot: Introduction Probability and Odds Single Event Probability and Odds Two and Multiple Event Experimental and Theoretical Probability Expected Value (Expected

### Unit 9: Probability Assignments

Unit 9: Probability Assignments #1: Basic Probability In each of exercises 1 & 2, find the probability that the spinner shown would land on (a) red, (b) yellow, (c) blue. 1. 2. Y B B Y B R Y Y B R 3. Suppose

### Name Class Date. Introducing Probability Distributions

Name Class Date Binomial Distributions Extension: Distributions Essential question: What is a probability distribution and how is it displayed? 8-6 CC.9 2.S.MD.5(+) ENGAGE Introducing Distributions Video

### out one marble and then a second marble without replacing the first. What is the probability that both marbles will be white?

Example: Leah places four white marbles and two black marbles in a bag She plans to draw out one marble and then a second marble without replacing the first What is the probability that both marbles will

### Practice 9-1. Probability

Practice 9-1 Probability You spin a spinner numbered 1 through 10. Each outcome is equally likely. Find the probabilities below as a fraction, decimal, and percent. 1. P(9) 2. P(even) 3. P(number 4. P(multiple

### * How many total outcomes are there if you are rolling two dice? (this is assuming that the dice are different, i.e. 1, 6 isn t the same as a 6, 1)

Compound probability and predictions Objective: Student will learn counting techniques * Go over HW -Review counting tree -All possible outcomes is called a sample space Go through Problem on P. 12, #2

### Name: Period: Date: 7 th Pre-AP: Probability Review and Mini-Review for Exam

Name: Period: Date: 7 th Pre-AP: Probability Review and Mini-Review for Exam 4. Mrs. Bartilotta s mathematics class has 7 girls and 3 boys. She will randomly choose two students to do a problem in front

### Name Date Class. Identify the sample space and the outcome shown for each experiment. 1. spinning a spinner

Name Date Class 0.5 Practice B Experimental Probability Identify the sample space and the outcome shown for each experiment.. spinning a spinner 2. tossing two coins Write impossible, unlikely, as likely

### Probability Test Review Math 2. a. What is? b. What is? c. ( ) d. ( )

Probability Test Review Math 2 Name 1. Use the following venn diagram to answer the question: Event A: Odd Numbers Event B: Numbers greater than 10 a. What is? b. What is? c. ( ) d. ( ) 2. In Jason's homeroom

### Counting Methods and Probability

CHAPTER Counting Methods and Probability Many good basketball players can make 90% of their free throws. However, the likelihood of a player making several free throws in a row will be less than 90%. You

### Compound Probability. A to determine the likelihood of two events occurring at the. ***Events can be classified as independent or dependent events.

Probability 68B A to determine the likelihood of two events occurring at the. ***Events can be classified as independent or dependent events. Independent Events are events in which the result of event

### Name. Is the game fair or not? Prove your answer with math. If the game is fair, play it 36 times and record the results.

Homework 5.1C You must complete table. Use math to decide if the game is fair or not. If Period the game is not fair, change the point system to make it fair. Game 1 Circle one: Fair or Not 2 six sided

### Welcome! U4H2: Worksheet # s 2-7, 9-13, 16, 20. Updates: U4T is 12/12. Announcement: December 16 th is the last day I will accept late work.

Welcome! U4H2: Worksheet # s 2-7, 9-13, 16, 20 Updates: U4T is 12/12 Announcement: December 16 th is the last day I will accept late work. 1 Review U4H1 2 Theoretical Probability 3 Experimental Probability

### What is the probability Jordan will pick a red marble out of the bag and land on the red section when spinning the spinner?

Name: Class: Date: Question #1 Jordan has a bag of marbles and a spinner. The bag of marbles has 10 marbles in it, 6 of which are red. The spinner is divided into 4 equal sections: blue, green, red, and

### MATH Student Book. 5th Grade Unit 3

MATH Student Book 5th Grade Unit 3 Unit 3 DIVIDING WHOLE NUMBERS AND DECIMALS MATH 503 DIVIDING WHOLE NUMBERS AND DECIMALS Introduction 3 1. One-Digit Divisors... 4 Estimating Quotients 11 Dividing Whole

### CHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY

CHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY Probability is the Probability is used in many real-world fields, such as insurance, medical research, law enforcement, and political science. Objectives:

### 7.1 Experiments, Sample Spaces, and Events

7.1 Experiments, Sample Spaces, and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment

### Lesson 3: Chance Experiments with Equally Likely Outcomes

Lesson : Chance Experiments with Equally Likely Outcomes Classwork Example 1 Jamal, a 7 th grader, wants to design a game that involves tossing paper cups. Jamal tosses a paper cup five times and records

### Independence Is The Word

Problem 1 Simulating Independent Events Describe two different events that are independent. Describe two different events that are not independent. The probability of obtaining a tail with a coin toss

### Applications. 28 How Likely Is It? P(green) = 7 P(yellow) = 7 P(red) = 7. P(green) = 7 P(purple) = 7 P(orange) = 7 P(yellow) = 7

Applications. A bucket contains one green block, one red block, and two yellow blocks. You choose one block from the bucket. a. Find the theoretical probability that you will choose each color. P(green)

### Compound Events. Identify events as simple or compound.

11.1 Compound Events Lesson Objectives Understand compound events. Represent compound events. Vocabulary compound event possibility diagram simple event tree diagram Understand Compound Events. A compound

### Chapter 8: Probability: The Mathematics of Chance

Chapter 8: Probability: The Mathematics of Chance Free-Response 1. A spinner with regions numbered 1 to 4 is spun and a coin is tossed. Both the number spun and whether the coin lands heads or tails is

### STATISTICS and PROBABILITY GRADE 6

Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition STATISTICS and PROBABILITY GRADE 6 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may use

### Unit 6: What Do You Expect? Investigation 2: Experimental and Theoretical Probability

Unit 6: What Do You Expect? Investigation 2: Experimental and Theoretical Probability Lesson Practice Problems Lesson 1: Predicting to Win (Finding Theoretical Probabilities) 1-3 Lesson 2: Choosing Marbles

### MATH STUDENT BOOK. 12th Grade Unit 5

MATH STUDENT BOOK 12th Grade Unit 5 Unit 5 ANALYTIC TRIGONOMETRY MATH 1205 ANALYTIC TRIGONOMETRY INTRODUCTION 3 1. IDENTITIES AND ADDITION FORMULAS 5 FUNDAMENTAL TRIGONOMETRIC IDENTITIES 5 PROVING IDENTITIES

### PRE TEST KEY. Math in a Cultural Context*

PRE TEST KEY Salmon Fishing: Investigations into A 6 th grade module in the Math in a Cultural Context* UNIVERSITY OF ALASKA FAIRBANKS Student Name: PRE TEST KEY Grade: Teacher: School: Location of School:

### Algebra 2 Notes Section 10.1: Apply the Counting Principle and Permutations

Algebra 2 Notes Section 10.1: Apply the Counting Principle and Permutations Objective(s): Vocabulary: I. Fundamental Counting Principle: Two Events: Three or more Events: II. Permutation: (top of p. 684)

### Grade 7/8 Math Circles February 25/26, Probability

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Probability Grade 7/8 Math Circles February 25/26, 2014 Probability Centre for Education in Mathematics and Computing Probability is the study of how likely

### Functional Skills Mathematics

Functional Skills Mathematics Level Learning Resource Probability D/L. Contents Independent Events D/L. Page - Combined Events D/L. Page - 9 West Nottinghamshire College D/L. Information Independent Events

### This Probability Packet Belongs to:

This Probability Packet Belongs to: 1 2 Station #1: M & M s 1. What is the sample space of your bag of M&M s? 2. Find the theoretical probability of the M&M s in your bag. Then, place the candy back into

### Lesson 17.1 Assignment

Lesson 17.1 Assignment Name Date Is It Better to Guess? Using Models for Probability Charlie got a new board game. 1. The game came with the spinner shown. 6 7 9 2 3 4 a. List the sample space for using

### PRE TEST. Math in a Cultural Context*

P grade PRE TEST Salmon Fishing: Investigations into A 6P th module in the Math in a Cultural Context* UNIVERSITY OF ALASKA FAIRBANKS Student Name: Grade: Teacher: School: Location of School: Date: *This

### Chapter 1: Sets and Probability

Chapter 1: Sets and Probability Section 1.3-1.5 Recap: Sample Spaces and Events An is an activity that has observable results. An is the result of an experiment. Example 1 Examples of experiments: Flipping

### Chapter 4: Probability

Student Outcomes for this Chapter Section 4.1: Contingency Tables Students will be able to: Relate Venn diagrams and contingency tables Calculate percentages from a contingency table Calculate and empirical

### 10.1 Applying the Counting Principle and Permutations (helps you count up the number of possibilities!)

10.1 Applying the Counting Principle and Permutations (helps you count up the number of possibilities!) Example 1: Pizza You are buying a pizza. You have a choice of 3 crusts, 4 cheeses, 5 meat toppings,

### Chapter 4: Probability and Counting Rules

Chapter 4: Probability and Counting Rules Before we can move from descriptive statistics to inferential statistics, we need to have some understanding of probability: Ch4: Probability and Counting Rules

### Section A Calculating Probabilities & Listing Outcomes Grade F D

Name: Teacher Assessment Section A Calculating Probabilities & Listing Outcomes Grade F D 1. A fair ordinary six-sided dice is thrown once. The boxes show some of the possible outcomes. Draw a line from