Algebra I Notes Unit One: Real Number System
|
|
- Randell Carter
- 5 years ago
- Views:
Transcription
1 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 on matrices. Teacher Note: A review of operations with real numbers should be incorporated throughout the first unit. Matrix: a rectangular arrangement of numbers in horizontal rows and vertical columns Entry (or element): each number in a matrix Order of a Matrix: number of rows number of columns = by Square Matrix: a matrix with the same number of rows as columns Ex: Ex: a. Find the order of the matrix. R R C1 C2 C This matrix has 2 rows and 3 columns. Therefore, its order is 2 3. (Read two by three.) b. Find the entry in the first row, second column in the matrix above The entry is 1. Matrices are used to organize data. Ex: Write a matrix to organize the following information regarding school lunch. A high school offers 5 entrees, 3 desserts, and 5 drinks. A middle school offers 3 entrees, 2 desserts, and 4 drinks. Ent Des Dri HS MS Question: What is another way to write this matrix? Adding and Subtracting Matrices: in order to add or subtract two matrices, they must have the same order. To add or subtract matrices, add or subtract the corresponding entries. Page 1 of 9 McDougal Littell: , 2.7, 2.8, 6.6, 6.7
2 Ex: Add the matrices , so we can find the sum. Note: Both matrices have the same order ( ) Note: Corresponding entries are the same color = Ex: Find the difference of the matrices. Note: Both matrices has the same order ( ) , so we can find the difference. It is helpful to rewrite the subtraction problem as addition (add the opposite) Now add the corresponding entries: = Scalar: a real number Multiplying by a Scalar: multiply every entry in the matrix by the scalar Ex: Find the product Multiply every entry by the scalar: = Page 2 of 9 McDougal Littell: , 2.7, 2.8, 6.6, 6.7
3 Using Matrices on the Graphing Calculator Ex: Find the sum and difference of the matrices on the graphing calculator , Use the MATRIX screen, then the EDIT menu to enter the matrices. Note that you must enter the order of the matrix (4 3. Keystrokes for Matrix A are below. Then enter the entries. ) To enter the second matrix, edit matrix B. Operations with the matrices can be calculated on the home screen. Below are the keystrokes for finding the sum: To view the rest of the matrix, use the right arrow to scroll over. Below are the keystrokes for finding the difference: You Try: Simplify by performing the operations QOD: Why must the orders of two matrices be the same to find the sum or difference? Page 3 of 9 McDougal Littell: , 2.7, 2.8, 6.6, 6.7
4 Syllabus Objective: 1.4 The student will determine the probability of an event with and without replacement using sample spaces. Probability of an Event: a number between 0 and 1, inclusive, that is a measure of the likelihood that the event will occur Note: An impossible event has a probability of 0, and a certain event has a probability of 1. Outcomes: the possible results of an experiment Event: a collection of outcomes Favorable Outcomes: the outcomes of an event that you wish to occur Calculating Theoretical Probability: P = # of Favorable Outcomes Total # of Outcomes Ex: What is the probability that you will roll an even number in one roll of a fair number cube? There are 3 even numbers on a number cube (2,4,and 6). These are the favorable outcomes. There are 6 numbers that are equally likely to roll on a number cube (1,2,3,4,5 and 6). These are the total outcomes. Therefore, the theoretical probability that you will roll an even number in one roll is Ex: Two coins are tossed. What is the probability that both are tails? List all of the possible outcomes when tossing two coins: HH, HT, TH, TT One of the outcomes is two tails. This is the favorable outcome. There are 4 possible outcomes that are equally likely. 3 1 P = = 6 2 Therefore, the theoretical probability that you will toss both tails is P = 1 4 Experimental Probability: the probability based on repetitions of an actual experiment Ex: Toss three coins 10 times and record the number of heads for each of the 10 tosses. Combine your results with the rest of the class. Find the experimental probability of getting three heads when three coins are tossed. Graphing Calculator: You can simulate a coin toss on the graphing calculator. Use the following keystrokes to begin the Probability Simulator: Page 4 of 9 McDougal Littell: , 2.7, 2.8, 6.6, 6.7
5 After collecting the data, compare the experimental probability with the theoretical probability. List all of the possible outcomes: HHH, HHT, HTT, HTH, THH, THT, TTH, TTT One of the outcomes is three heads. This is the favorable outcome. Therefore, the theoretical probability of obtaining three heads is P = 1 8 Probability of Two Events: calculate the product of the theoretical probabilities Ex: Find the probability of obtaining a head and rolling a 5 when tossing a coin and rolling a die. Probability of tossing a head: 1 2 Probability of rolling a 5: 1 6 Probability of tossing a head and rolling a 5: 1 1 = Note: You may also write out all of the possible outcomes. Probability With and Without Replacement Ex: A drawer has 6 blue socks, 4 red socks, and 10 white socks. Find the probability of randomly picking a blue sock and then a red sock out of the drawer if you replace the first sock after it is picked. Probability of picking a blue sock: 6 3 = Probability of picking a red sock: = 20 5 Probability of picking a blue sock and then a red sock (with replacement): 3 1 = Ex: A drawer has 6 blue socks, 4 red socks, and 10 white socks. Find the probability of randomly picking a blue sock and then a red sock out of the drawer if you do not replace the first sock after it is picked. Probability of picking a blue sock: 6 3 = Probability of picking a red sock (if the first sock, which is blue, is NOT replaced): 4 19 Probability of picking a blue sock and then a red sock (without replacement): 3 4 = 3 2 = Page 5 of 9 McDougal Littell: , 2.7, 2.8, 6.6, 6.7
6 You Try: Find the probability of randomly choosing an M from the letters in the word MATHEMATICS. QOD: The probability of one event is 2 3. The probability of a second event is 3. Which event is more 8 likely to occur? Page 6 of 9 McDougal Littell: , 2.7, 2.8, 6.6, 6.7
7 Syllabus Objective: 1.3 The student will collect, organize, display, and analyze data using graphical representations including box and whisker plots. Measures of Central Tendency: a number used to represent a typical value in a set of data. There are three commonly used measures of central tendency: Mean (average): the sum of the data values divided by the number of data values Median: the middle number when the data values are written in order Note: If there are two numbers in the middle, the average of these two numbers is the median. Mode: the data value(s) that occurs most often Note: A set of data may have more than one mode or no mode. Ex: Find the mean, median, and mode of the set of data. 45,1,52, 42,10, 40,50, 40,7,52 Mean: = 339 = Median: Put values in order 1,7,10,40,40,42,45,50,52,52 40,4There are two numbers the middle 1,7,10, 40,, 45,50,52,52 the average of the two middle numbers. 2Find = 82 = Mode: There are two values that occur the most, 40 and 52. Stem-and-Leaf Plot: an arrangement of digits used to display numerical data in order Ex: Create a stem-and-leaf plot for the data in the example above. Use the digits in the tens place for the stems and the digits in the ones place for the leaves. Note: We will include all of the tens places from 0 to Key: 52 represents the number 52. Box-and-Whisker Plot: a data display that divides a set of data into four parts Median (Second Quartile): the middle number of a set of data that is written in order First Quartile: the median of the lower half of the data Third Quartile: the median of the upper half of the data Page 7 of 9 McDougal Littell: , 2.7, 2.8, 6.6, 6.7
8 Range: the difference between the largest and smallest data values Interquartile Range (IQR): the difference between the Third and First Quartiles Ex: Use the set of data 10, 20, 5, 34, 9, 25, 28, 15, 16, 12, 13, 7 to draw a box-and-whisker plot. Then find the range and IQR. Step One: Put the data values in order. 5, 7, 9, 11, 12, 13, 15, 16, 21, 25, 28, 34 Step Two: Find the three quartiles Second Quartile (median): Q2 = = = First Quartile: 5,7,9,11,12,13, 15,16,21,25,28, Median of lower half: Q1 = = = Third Quartile: 5,7,9,11,12,13, 15,16,21,25,28, Median of upper half: Q3 = = = Step Three: Draw the box-and-whisker plot above a number line. Label the number line according to the data values. Note: The whiskers connect the box to the smallest and largest numbers in the data set. The number line above begins at 0 and ends at 35 with a scale of 5. Range: 34 5 = 29 IQR: = 13 Ex: Use the box-and-whisker plot above to answer the following questions: 1. What percent of the data is located within the box? Solution: Each piece of the box is 25% of the data, which means 50% of the data lie within the box. 2. What fraction of the data are less than 23? Solution: 23 is the third quartile, so 3 quarters of the data lie below it. Therefore, the fraction is What percent of the data are greater than 10? Solution: 10 is the first quartile, which means 25% (a quarter) of the data are less than 10. Therefore, 75% of the data are greater than 10. Page 8 of 9 McDougal Littell: , 2.7, 2.8, 6.6, 6.7
9 You Try: Use the data in the stem-and-leaf plot to create a box-and-whisker plot. Find the measures of central tendency, the range, and the interquartile range. You may use your calculator for computation Key: 16 4 = 164 QOD: Describe a set of data that would have no mode. Page 9 of 9 McDougal Littell: , 2.7, 2.8, 6.6, 6.7
TJP TOP TIPS FOR IGCSE STATS & PROBABILITY
TJP TOP TIPS FOR IGCSE STATS & PROBABILITY Dr T J Price, 2011 First, some important words; know what they mean (get someone to test you): Mean the sum of the data values divided by the number of items.
More informationUNIT 4 APPLICATIONS OF PROBABILITY Lesson 1: Events. Instruction. Guided Practice Example 1
Guided Practice Example 1 Bobbi tosses a coin 3 times. What is the probability that she gets exactly 2 heads? Write your answer as a fraction, as a decimal, and as a percent. Sample space = {HHH, HHT,
More informationMath 146 Statistics for the Health Sciences Additional Exercises on Chapter 3
Math 46 Statistics for the Health Sciences Additional Exercises on Chapter 3 Student Name: Find the indicated probability. ) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH
More informationGrade 6 Math Circles Fall Oct 14/15 Probability
1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 6 Math Circles Fall 2014 - Oct 14/15 Probability Probability is the likelihood of an event occurring.
More informationAlgebra 2 P49 Pre 10 1 Measures of Central Tendency Box and Whisker Plots Variation and Outliers
Algebra 2 P49 Pre 10 1 Measures of Central Tendency Box and Whisker Plots Variation and Outliers 10 1 Sample Spaces and Probability Mean Average = 40/8 = 5 Measures of Central Tendency 2,3,3,4,5,6,8,9
More information= = 0.1%. On the other hand, if there are three winning tickets, then the probability of winning one of these winning tickets must be 3 (1)
MA 5 Lecture - Binomial Probabilities Wednesday, April 25, 202. Objectives: Introduce combinations and Pascal s triangle. The Fibonacci sequence had a number pattern that we could analyze in different
More informationProbability and Statistics. Copyright Cengage Learning. All rights reserved.
Probability and Statistics Copyright Cengage Learning. All rights reserved. 14.2 Probability Copyright Cengage Learning. All rights reserved. Objectives What Is Probability? Calculating Probability by
More informationProbability Assignment
Name Probability Assignment Student # Hr 1. An experiment consists of spinning the spinner one time. a. How many possible outcomes are there? b. List the sample space for the experiment. c. Determine the
More informationMATH STUDENT BOOK. 7th Grade Unit 6
MATH STUDENT BOOK 7th Grade Unit 6 Unit 6 Probability and Graphing Math 706 Probability and Graphing Introduction 3 1. Probability 5 Theoretical Probability 5 Experimental Probability 13 Sample Space 20
More informationChapter 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
More information3. a. P(white) =, or. b. ; the probability of choosing a white block. d. P(white) =, or. 4. a. = 1 b. 0 c. = 0
Answers Investigation ACE Assignment Choices Problem. Core, 6 Other Connections, Extensions Problem. Core 6 Other Connections 7 ; unassigned choices from previous problems Problem. Core 7 9 Other Connections
More informationFALL 2012 MATH 1324 REVIEW EXAM 4
FALL 01 MATH 134 REVIEW EXAM 4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the sample space for the given experiment. 1) An ordinary die
More information1) What is the total area under the curve? 1) 2) What is the mean of the distribution? 2)
Math 1090 Test 2 Review Worksheet Ch5 and Ch 6 Name Use the following distribution to answer the question. 1) What is the total area under the curve? 1) 2) What is the mean of the distribution? 2) 3) Estimate
More informationLesson 10: Using Simulation to Estimate a Probability
Lesson 10: Using Simulation to Estimate a Probability Classwork In previous lessons, you estimated probabilities of events by collecting data empirically or by establishing a theoretical probability model.
More informationProbability 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
More informationProbability: Terminology and Examples Spring January 1, / 22
Probability: Terminology and Examples 18.05 Spring 2014 January 1, 2017 1 / 22 Board Question Deck of 52 cards 13 ranks: 2, 3,..., 9, 10, J, Q, K, A 4 suits:,,,, Poker hands Consists of 5 cards A one-pair
More informationProbability. 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
More informationBellwork Write each fraction as a percent Evaluate P P C C 6
Bellwork 2-19-15 Write each fraction as a percent. 1. 2. 3. 4. Evaluate. 5. 6 P 3 6. 5 P 2 7. 7 C 4 8. 8 C 6 1 Objectives Find the theoretical probability of an event. Find the experimental probability
More informationDescriptive Statistics II. Graphical summary of the distribution of a numerical variable. Boxplot
MAT 2379 (Spring 2012) Descriptive Statistics II Graphical summary of the distribution of a numerical variable We will present two types of graphs that can be used to describe the distribution of a numerical
More informationGrade 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
More informationSTAT 430/510 Probability Lecture 3: Space and Event; Sample Spaces with Equally Likely Outcomes
STAT 430/510 Probability Lecture 3: Space and Event; Sample Spaces with Equally Likely Outcomes Pengyuan (Penelope) Wang May 25, 2011 Review We have discussed counting techniques in Chapter 1. (Principle
More informationNow 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
More informationb. 2 ; the probability of choosing a white d. P(white) 25, or a a. Since the probability of choosing a
Applications. a. P(green) =, P(yellow) = 2, or 2, P(red) = 2 ; three of the four blocks are not red. d. 2. a. P(green) = 2 25, P(purple) = 6 25, P(orange) = 2 25, P(yellow) = 5 25, or 5 2 6 2 5 25 25 25
More informationShe concludes that the dice is biased because she expected to get only one 6. Do you agree with June's conclusion? Briefly justify your answer.
PROBABILITY & STATISTICS TEST Name: 1. June suspects that a dice may be biased. To test her suspicions, she rolls the dice 6 times and rolls 6, 6, 4, 2, 6, 6. She concludes that the dice is biased because
More informationName 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
More informationNumberSense Companion Workbook Grade 4
NumberSense Companion Workbook Grade 4 Sample Pages (ENGLISH) Working in the NumberSense Companion Workbook The NumberSense Companion Workbooks address measurement, spatial reasoning (geometry) and data
More informationMath 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
More informationEECS 203 Spring 2016 Lecture 15 Page 1 of 6
EECS 203 Spring 2016 Lecture 15 Page 1 of 6 Counting We ve been working on counting for the last two lectures. We re going to continue on counting and probability for about 1.5 more lectures (including
More informationWhat are the chances?
What are the chances? Student Worksheet 7 8 9 10 11 12 TI-Nspire Investigation Student 90 min Introduction In probability, we often look at likelihood of events that are influenced by chance. Consider
More informationHeads Up! A c t i v i t y 5. The Problem. Name Date
. Name Date A c t i v i t y 5 Heads Up! In this activity, you will study some important concepts in a branch of mathematics known as probability. You are using probability when you say things like: It
More informationProbability. Ms. Weinstein Probability & Statistics
Probability Ms. Weinstein Probability & Statistics Definitions Sample Space The sample space, S, of a random phenomenon is the set of all possible outcomes. Event An event is a set of outcomes of a random
More informationCounting methods (Part 4): More combinations
April 13, 2009 Counting methods (Part 4): More combinations page 1 Counting methods (Part 4): More combinations Recap of last lesson: The combination number n C r is the answer to this counting question:
More information12.1 The Fundamental Counting Principle and Permutations
12.1 The Fundamental Counting Principle and Permutations The Fundamental Counting Principle Two Events: If one event can occur in ways and another event can occur in ways then the number of ways both events
More informationName: Class: Date: Probability/Counting Multiple Choice Pre-Test
Name: _ lass: _ ate: Probability/ounting Multiple hoice Pre-Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1 The dartboard has 8 sections of equal area.
More informationNAME 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.
More informationCS 361: Probability & Statistics
January 31, 2018 CS 361: Probability & Statistics Probability Probability theory Probability Reasoning about uncertain situations with formal models Allows us to compute probabilities Experiments will
More informationWhat is the expected number of rolls to get a Yahtzee?
Honors Precalculus The Yahtzee Problem Name Bolognese Period A Yahtzee is rolling 5 of the same kind with 5 dice. The five dice are put into a cup and poured out all at once. Matching dice are kept out
More informationTo describe the centre and spread of a univariate data set by way of a 5-figure summary and visually by a box & whisker plot.
Five Figure Summary Teacher Notes & Answers 7 8 9 10 11 12 TI-Nspire Investigation Student 60 min Aim To describe the centre and spread of a univariate data set by way of a 5-figure summary and visually
More informationDiamond ( ) (Black coloured) (Black coloured) (Red coloured) ILLUSTRATIVE EXAMPLES
CHAPTER 15 PROBABILITY Points to Remember : 1. In the experimental approach to probability, we find the probability of the occurence of an event by actually performing the experiment a number of times
More informationIntro to Algebra Guided Notes (Unit 11)
Intro to Algebra Guided Notes (Unit 11) PA 12-1, 12-2, 12-3, 12-7 Alg 12-2, 12-3, 12-4 NAME 12-1 Stem-and-Leaf Plots Stem-and-Leaf Plot: numerical data are listed in ascending or descending order. The
More informationMath 7 Notes - Unit 11 Probability
Math 7 Notes - Unit 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 theoretical
More informationWhat 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
More informationheads 1/2 1/6 roll a die sum on 2 dice 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 1, 2, 3, 4, 5, 6 heads tails 3/36 = 1/12 toss a coin trial: an occurrence
trial: an occurrence roll a die toss a coin sum on 2 dice sample space: all the things that could happen in each trial 1, 2, 3, 4, 5, 6 heads tails 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 example of an outcome:
More informationUnit 8, Activity 1, Vocabulary Self-Awareness Chart
Unit 8, Activity 1, Vocabulary Self-Awareness Chart Vocabulary Self-Awareness Chart WORD +? EXAMPLE DEFINITION Central Tendency Mean Median Mode Range Quartile Interquartile Range Standard deviation Stem
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1332 Review Test 4 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem by applying the Fundamental Counting Principle with two
More informationSTAT 155 Introductory Statistics. Lecture 11: Randomness and Probability Model
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Lecture 11: Randomness and Probability Model 10/5/06 Lecture 11 1 The Monty Hall Problem Let s Make A Deal: a game show
More informationTEKSING 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.
More informationData Analysis and Probability
CHAPTER 1 Data Analysis and Probability Solutions Key ARe you ready? 1. D. B. F. E. A. x 1 x x 9 x 7. 1 9 x. 1 x 1 1x 7 1x 1 1 x 7 1 1 x x 1. x 9. 1 x 1 1. > 1, 1x, 1 1x 1 1 x 11. > 1 1. < 7 9 1..7 9 1.
More informationTenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7
EngageNY Module 1: Ratios and Proportional Relationships Topic A: Proportional Relationships Lesson 1 Lesson 2 Lesson 3 Understand equivalent ratios, rate, and unit rate related to a Understand proportional
More informationAlgebra I Notes Unit Seven: Writing Linear Equations
Sllabus Objective.6 The student will be able to write the equation of a linear function given two points, a point and the slope, table of values, or a graphical representation. Slope-Intercept Form of
More informationSections Descriptive Statistics for Numerical Variables
Math 243 Sections 2.1.2-2.2.5 Descriptive Statistics for Numerical Variables A framework to describe quantitative data: Describe the Shape, Center and Spread, and Unusual Features Shape How is the data
More informationSTOR 155 Introductory Statistics. Lecture 10: Randomness and Probability Model
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics Lecture 10: Randomness and Probability Model 10/6/09 Lecture 10 1 The Monty Hall Problem Let s Make A Deal: a game show
More informationNumerical: Data with quantity Discrete: whole number answers Example: How many siblings do you have?
Types of data Numerical: Data with quantity Discrete: whole number answers Example: How many siblings do you have? Continuous: Answers can fall anywhere in between two whole numbers. Usually any type of
More informationHPS Scope Sequence Last Revised June SUBJECT: Math GRADE: 7. Michigan Standard (GLCE) Code & Language. What this Standard means:
Number and Numeration MA.7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical
More informationProbability --QUESTIONS-- Principles of Math 12 - Probability Practice Exam 1
Probability --QUESTIONS-- Principles of Math - Probability Practice Exam www.math.com Principles of Math : Probability Practice Exam Use this sheet to record your answers:... 4... 4... 4.. 6. 4.. 6. 7..
More informationUnit 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
More informationCCM6+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
More informationProbability Exercise 2
Probability Exercise 2 1 Question 9 A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will
More informationLesson 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
More informationgreen, green, green, green, green The favorable outcomes of the event are blue and red.
5 Chapter Review Review Key Vocabulary experiment, p. 6 outcomes, p. 6 event, p. 6 favorable outcomes, p. 6 probability, p. 60 relative frequency, p. 6 Review Examples and Exercises experimental probability,
More informationFdaytalk.com. Outcomes is probable results related to an experiment
EXPERIMENT: Experiment is Definite/Countable probable results Example: Tossing a coin Throwing a dice OUTCOMES: Outcomes is probable results related to an experiment Example: H, T Coin 1, 2, 3, 4, 5, 6
More informationCompound 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
More informationWhen 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
More informationHomework #1-19: Use the Counting Principle to answer the following questions.
Section 4.3: Tree Diagrams and the Counting Principle Homework #1-19: Use the Counting Principle to answer the following questions. 1) If two dates are selected at random from the 365 days of the year
More informationLesson 8: The Difference Between Theoretical Probabilities and Estimated Probabilities
Lesson 8: The Difference Between Theoretical Probabilities and Estimated Probabilities Did you ever watch the beginning of a Super Bowl game? After the traditional handshakes, a coin is tossed to determine
More informationMaking Middle School Math Come Alive with Games and Activities
Making Middle School Math Come Alive with Games and Activities For more information about the materials you find in this packet, contact: Sharon Rendon (605) 431-0216 sharonrendon@cpm.org 1 2-51. SPECIAL
More informationProbability is often written as a simplified fraction, but it can also be written as a decimal or percent.
CHAPTER 1: PROBABILITY 1. Introduction to Probability L EARNING TARGET: I CAN DETERMINE THE PROBABILITY OF AN EVENT. What s the probability of flipping heads on a coin? Theoretically, it is 1/2 1 way to
More informationChapter 4: Introduction to Probability
MTH 243 Chapter 4: Introduction to Probability Suppose that we found that one of our pieces of data was unusual. For example suppose our pack of M&M s only had 30 and that was 3.1 standard deviations below
More informationName: 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,
More informationPart 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:
More informationMATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING DR. DAVID BRIDGE
MATH 205 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM # - SPRING 2006 - DR. DAVID BRIDGE TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Tell whether the statement is
More informationEssentials. Week by. Week. Calculate! What is the largest product you can compute on your calculator? largest quotient?
Week by Week MATHEMATICS Essentials Grade WEEK 5 Calculate! What is the largest product you can compute on your calculator? largest quotient? Is the answer the same for all the calculators in your class?
More informationAlgebra II- Chapter 12- Test Review
Sections: Counting Principle Permutations Combinations Probability Name Choose the letter of the term that best matches each statement or phrase. 1. An illustration used to show the total number of A.
More informationExercise Class XI Chapter 16 Probability Maths
Exercise 16.1 Question 1: Describe the sample space for the indicated experiment: A coin is tossed three times. A coin has two faces: head (H) and tail (T). When a coin is tossed three times, the total
More informationMaking Middle School Math Come Alive with Games and Activities
Making Middle School Math Come Alive with Games and Activities For more information about the materials you find in this packet, contact: Chris Mikles 916-719-3077 chrismikles@cpm.org 1 2 2-51. SPECIAL
More informationMath 147 Elementary Probability/Statistics I Additional Exercises on Chapter 4: Probability
Math 147 Elementary Probability/Statistics I Additional Exercises on Chapter 4: Probability Student Name: Find the indicated probability. 1) If you flip a coin three times, the possible outcomes are HHH
More informationSTATISTICS 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
More information1. Answer (B): Brianna is half as old as Aunt Anna, so Brianna is 21 years old. Caitlin is 5 years younger than Brianna, so Caitlin is 16 years old.
Solutions 2000 6 th AMC 8 2. Answer (B): Brianna is half as old as Aunt Anna, so Brianna is 2 years old. Caitlin is 5 years younger than Brianna, so Caitlin is 6 years old. 2. Answer (A): The number 0
More information12 Probability. Introduction Randomness
2 Probability Assessment statements 5.2 Concepts of trial, outcome, equally likely outcomes, sample space (U) and event. The probability of an event A as P(A) 5 n(a)/n(u ). The complementary events as
More informationProbability. Dr. Zhang Fordham Univ.
Probability! Dr. Zhang Fordham Univ. 1 Probability: outline Introduction! Experiment, event, sample space! Probability of events! Calculate Probability! Through counting! Sum rule and general sum rule!
More informationTEKSING TOWARD STAAR MATHEMATICS GRADE 6. Student Book
TEKSING TOWARD STAAR MATHEMATICS GRADE 6 Student Book TEKSING TOWARD STAAR 2014 Six Weeks 1 Lesson 1 STAAR Category 1 Grade 6 Mathematics TEKS 6.2A/6.2B Problem-Solving Model Step Description of Step 1
More informationSAMPLE. This chapter deals with the construction and interpretation of box plots. At the end of this chapter you should be able to:
find the upper and lower extremes, the median, and the upper and lower quartiles for sets of numerical data calculate the range and interquartile range compare the relative merits of range and interquartile
More informationIn how many ways can the letters of SEA be arranged? In how many ways can the letters of SEE be arranged?
-Pick up Quiz Review Handout by door -Turn to Packet p. 5-6 In how many ways can the letters of SEA be arranged? In how many ways can the letters of SEE be arranged? - Take Out Yesterday s Notes we ll
More informationChapter 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
More informationUNIT 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.
More informationSection 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
More informationName: 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
More informationCore Connections, Course 2 Checkpoint Materials
Core Connections, Course Checkpoint Materials Notes to Students (and their Teachers) Students master different skills at different speeds. No two students learn exactly the same way at the same time. At
More informationRANDOM EXPERIMENTS AND EVENTS
Random Experiments and Events 18 RANDOM EXPERIMENTS AND EVENTS In day-to-day life we see that before commencement of a cricket match two captains go for a toss. Tossing of a coin is an activity and getting
More informationA B C. 142 D. 96
Data Displays and Analysis 1. stem leaf 900 3 3 4 5 7 9 901 1 1 1 2 4 5 6 7 8 8 8 9 9 902 1 3 3 3 4 6 8 9 9 903 1 2 2 3 3 3 4 7 8 9 904 1 1 2 4 5 6 8 8 What is the range of the data shown in the stem-and-leaf
More informationExam Time. Final Exam Review. TR class Monday December 9 12:30 2:30. These review slides and earlier ones found linked to on BlackBoard
Final Exam Review These review slides and earlier ones found linked to on BlackBoard Bring a photo ID card: Rocket Card, Driver's License Exam Time TR class Monday December 9 12:30 2:30 Held in the regular
More informationAdriana tosses a number cube with faces numbered 1 through 6 and spins the spinner shown below at the same time.
Domain 5 Lesson 9 Compound Events Common Core Standards: 7.SP.8.a, 7.SP.8.b, 7.SP.8.c Getting the Idea A compound event is a combination of two or more events. Compound events can be dependent or independent.
More informationProbability. 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
More information3.6 Theoretical and Experimental Coin Tosses
wwwck12org Chapter 3 Introduction to Discrete Random Variables 36 Theoretical and Experimental Coin Tosses Here you ll simulate coin tosses using technology to calculate experimental probability Then you
More informationName. 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
More informationPROBABILITY COMPACTED MATHEMATICS CHAPTER 14 TOPICS COVERED:
PROBABILITY COMPACTED MATHEMATICS CHAPTER 14 PROBABILITY TOPICS COVERED: Basic Probability Finding Outcomes Tree Diagrams and Tables with Independent Events Theoretical vs. Experimental Probability Activity
More informationCPM Educational Program
CC COURSE 2 ETOOLS Table of Contents General etools... 5 Algebra Tiles (CPM)... 6 Pattern Tile & Dot Tool (CPM)... 9 Area and Perimeter (CPM)...11 Base Ten Blocks (CPM)...14 +/- Tiles & Number Lines (CPM)...16
More informationFAVORITE MEALS NUMBER OF PEOPLE Hamburger and French fries 17 Spaghetti 8 Chili 12 Vegetarian delight 3
Probability 1. Destiny surveyed customers in a restaurant to find out their favorite meal. The results of the survey are shown in the table. One person in the restaurant will be picked at random. Based
More informationClass XII Chapter 13 Probability Maths. Exercise 13.1
Exercise 13.1 Question 1: Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E F) = 0.2, find P (E F) and P(F E). It is given that P(E) = 0.6, P(F) = 0.3, and P(E F) = 0.2 Question 2:
More information(Notice that the mean doesn t have to be a whole number and isn t normally part of the original set of data.)
One-Variable Statistics Descriptive statistics that analyze one characteristic of one sample Where s the middle? How spread out is it? Where do different pieces of data compare? To find 1-variable statistics
More information