Tree Diagrams and the Fundamental Counting Principle
|
|
- Aron George
- 5 years ago
- Views:
Transcription
1 Objective: In this lesson, you will use permutations and combinations to compute probabilities of compound events and to solve problems. Read this knowledge article and answer the following: Tree Diagrams and the Fundamental Counting Principle Example 1 If a woman has two blouses {B1, B2} and three skirts {s1, s2, s3}, how many different outfits consisting of a blouse and a skirt can she wear? The fundamental counting principle states that if one task can be done in m ways, and a second task can be done in n ways, then Example 2 A truck license plate consists of a letter followed by four digits. How many such license plates are possible? Determining Probability with the Fundamental Counting Principle Example 3 A truck license plate consists of a letter followed by four digits. If you select one license plate at random, what is the probability it contains the letter Z? Page 1
2 Permutations Find the number of sequences that can be formed with the letters {A. B, C} if no letter is repeated. Draw a tree diagram to determine the number of sequences. The tree diagram gives us Use the fundamental counting principle to determine the number of sequences. We have three choices for the, two choices for the, and one choice for the. The fundamental counting principle gives us. We can write this equation using factorial notation as Factorial notation is defined as n! = 1! = 1 and 0! = 1 Where order is important and no element is repeated are permutations. A permutation of a set of elements is an ordered arrangement where each element is used once. Example 4 Given five letters {A, B, C, D, E}, find the number of four-letter sequences possible. Permutations of n objects taken r at a time is written as. Example 4 can also be answered as: The number of four-letter sequences is = 5P4 = 120. Page 2
3 Example 6 You have 4 math books and 5 history books to put on a shelf that has 5 slots. In how many ways can the books be shelved if the first three slots are filled with math books and the next two slots are filled with history books? First we determine the number of ways the math books can be arranged. This is a permutation of 4 objects taken 3 at a time, or 4P3: 4P3 = Next we determine the number of ways the history books can be arranged. This is a permutation of 5 objects taken 2 at a time, or 5P2: 5P2 = Since there are 24 ways to arrange the math books and 20 ways to arrange the history books, the total number of ways to arrange the math and history books is Page 3
4 Combinations Suppose that we have a set of three letters {A, B, C}, and we are asked to make two-letter sequences. We have six permutations: AB BA BC CB AC CA Now suppose we have a group of three people {A, B, C}, Al, Bob, and Chris, respectively, and we are asked to form committees of two people each. This time we have only three committees: AB BC AC When forming committees, the order is not important because the committee that has Al and Bob is no different from the committee that has Bob and Al. As a result, we have only three committees, not six. Forming sequences is an example of permutations. Forming committees is an example of combinations. Permutations are those arrangements where Combinations are those arrangements where ncr represents the number of combinations of n objects taken r at a time. Page 4
5 Combinations Involving Several Sets Example 8 How many five-person committees consisting of 2 men and 3 women can be chosen from a group of 4 men and 4 women? First we consider the number of combinations of 4 men chosen 2 at a time: Next we consider the number of combinations of 4 women chosen 3 at a time: 6 4 = Probabilities Involving Combinations Example 9 A high school club consists of 4 freshmen, 5 sophomores, 5 juniors, and 6 seniors. What is the probability that a committee of 4 people chosen at random includes one student from each class? The total number of committees possible is 20C4 since there are 20 students in all and we want to select 4: 20C4 = 4,845 The number of combinations of 4 freshman taken 1 at a time is The number of combinations of 5 sophomores taken 1 at a time is The number of combinations of 5 juniors taken 1 at a time is The number of combinations of 6 juniors taken 1 at a time is = Example 10 A high school club consists of 4 freshmen, 5 sophomores, 5 juniors, and 6 seniors. What is the probability that a committee of 4 people chosen at random includes at least one senior? P (at least one senior) = = Page 5
6 Example Page 6
Chapter 11, Sets and Counting from Applied Finite Mathematics by Rupinder Sekhon was developed by OpenStax College, licensed by Rice University, and
Chapter 11, Sets and Counting from Applied Finite Mathematics by Rupinder Sekhon was developed by OpenStax College, licensed by Rice University, and is available on the Connexions website. It is used under
More informationUsing a table: regular fine micro. red. green. The number of pens possible is the number of cells in the table: 3 2.
Counting Methods: Example: A pen has tip options of regular tip, fine tip, or micro tip, and it has ink color options of red ink or green ink. How many different pens are possible? Using a table: regular
More informationPermutations and Combinations Problems
Permutations and Combinations Problems Permutations and combinations are used to solve problems. Factorial Example 1: How many 3 digit numbers can you make using the digits 1, 2 and 3 without method (1)
More informationFundamentals of Probability
Fundamentals of Probability Introduction Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1. An impossible
More informationMath 166: Topics in Contemporary Mathematics II
Math 166: Topics in Contemporary Mathematics II Xin Ma Texas A&M University September 30, 2017 Xin Ma (TAMU) Math 166 September 30, 2017 1 / 11 Last Time Factorials For any natural number n, we define
More informationMath 14 Lecture Notes Ch. 3.6
Math Lecture Notes h... ounting Rules xample : Suppose a lottery game designer wants to list all possible outcomes of the following sequences of events: a. tossing a coin once and rolling a -sided die
More informationFinite Math - Fall 2016
Finite Math - Fall 206 Lecture Notes - /28/206 Section 7.4 - Permutations and Combinations There are often situations in which we have to multiply many consecutive numbers together, for example, in examples
More informationSTAT 430/510 Probability
STAT 430/510 Probability Hui Nie Lecture 1 May 26th, 2009 Introduction Probability is the study of randomness and uncertainty. In the early days, probability was associated with games of chance, such as
More informationName: Exam 1. September 14, 2017
Department of Mathematics University of Notre Dame Math 10120 Finite Math Fall 2017 Name: Instructors: Basit & Migliore Exam 1 September 14, 2017 This exam is in two parts on 9 pages and contains 14 problems
More information50 Counting Questions
50 Counting Questions Prob-Stats (Math 3350) Fall 2012 Formulas and Notation Permutations: P (n, k) = n!, the number of ordered ways to permute n objects into (n k)! k bins. Combinations: ( ) n k = n!,
More informationJessica Fauser EDUC 352 October 21, 2011 Unit Lesson Plan #3. Lesson: Permutations and Combinations Length: 45 minutes Age/Grade Intended: Algebra II
Jessica Fauser EDUC 352 October 21, 2011 Unit Lesson Plan #3 Lesson: Permutations and Combinations Length: 45 minutes Age/Grade Intended: Algebra II Academic Standard(s): A2.8.4 Use permutations, combinations,
More informationPermutations. and. Combinations
Permutations and Combinations Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another independent event has n possible outcomes, then there
More informationCourse Learning Outcomes for Unit V
UNIT V STUDY GUIDE Counting Reading Assignment See information below. Key Terms 1. Combination 2. Fundamental counting principle 3. Listing 4. Permutation 5. Tree diagrams Course Learning Outcomes for
More informationCHAPTER 8 Additional Probability Topics
CHAPTER 8 Additional Probability Topics 8.1. Conditional Probability Conditional probability arises in probability experiments when the person performing the experiment is given some extra information
More informationW = {Carrie (U)nderwood, Kelly (C)larkson, Chris (D)aughtry, Fantasia (B)arrino, and Clay (A)iken}
UNIT V STUDY GUIDE Counting Course Learning Outcomes for Unit V Upon completion of this unit, students should be able to: 1. Apply mathematical principles used in real-world situations. 1.1 Draw tree diagrams
More informationFundamental Counting Principle
Lesson 88 Probability with Combinatorics HL2 Math - Santowski Fundamental Counting Principle Fundamental Counting Principle can be used determine the number of possible outcomes when there are two or more
More information4.3 Rules of Probability
4.3 Rules of Probability If a probability distribution is not uniform, to find the probability of a given event, add up the probabilities of all the individual outcomes that make up the event. Example:
More information7.4 Permutations and Combinations
7.4 Permutations and Combinations The multiplication principle discussed in the preceding section can be used to develop two additional counting devices that are extremely useful in more complicated counting
More informationFinite Mathematics MAT 141: Chapter 8 Notes
Finite Mathematics MAT 4: Chapter 8 Notes Counting Principles; More David J. Gisch The Multiplication Principle; Permutations Multiplication Principle Multiplication Principle You can think of the multiplication
More informationCOUNTING AND PROBABILITY
CHAPTER 9 COUNTING AND PROBABILITY Copyright Cengage Learning. All rights reserved. SECTION 9.2 Possibility Trees and the Multiplication Rule Copyright Cengage Learning. All rights reserved. Possibility
More informationIn this section, we will learn to. 1. Use the Multiplication Principle for Events. Cheesecake Factory. Outback Steakhouse. P.F. Chang s.
Section 10.6 Permutations and Combinations 10-1 10.6 Permutations and Combinations In this section, we will learn to 1. Use the Multiplication Principle for Events. 2. Solve permutation problems. 3. Solve
More informationMath 227 Elementary Statistics. Bluman 5 th edition
Math 227 Elementary Statistics Bluman 5 th edition CHAPTER 4 Probability and Counting Rules 2 Objectives Determine sample spaces and find the probability of an event using classical probability or empirical
More informationSTAT 430/510 Probability Lecture 1: Counting-1
STAT 430/510 Probability Lecture 1: Counting-1 Pengyuan (Penelope) Wang May 22, 2011 Introduction In the early days, probability was associated with games of chance, such as gambling. Probability is describing
More informationExamples: Experiment Sample space
Intro to Probability: A cynical person once said, The only two sure things are death and taxes. This philosophy no doubt arose because so much in people s lives is affected by chance. From the time a person
More information4.1 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
More informationUnit on Permutations and Combinations (Counting Techniques)
Page 1 of 15 (Edit by Y.M. LIU) Page 2 of 15 (Edit by Y.M. LIU) Unit on Permutations and Combinations (Counting Techniques) e.g. How many different license plates can be made that consist of three digits
More informationUnit Nine Precalculus Practice Test Probability & Statistics. Name: Period: Date: NON-CALCULATOR SECTION
Name: Period: Date: NON-CALCULATOR SECTION Vocabulary: Define each word and give an example. 1. discrete mathematics 2. dependent outcomes 3. series Short Answer: 4. Describe when to use a combination.
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 informationPermutation and Combination
BANKERSWAY.COM Permutation and Combination Permutation implies arrangement where order of things is important. It includes various patterns like word formation, number formation, circular permutation etc.
More informationElementary Combinatorics
184 DISCRETE MATHEMATICAL STRUCTURES 7 Elementary Combinatorics 7.1 INTRODUCTION Combinatorics deals with counting and enumeration of specified objects, patterns or designs. Techniques of counting are
More informationSets, Venn Diagrams & Counting
MT 142 College Mathematics Sets, Venn Diagrams & Counting Module SC Terri Miller revised December 13, 2010 What is a set? Sets set is a collection of objects. The objects in the set are called elements
More informationUnit 5, Activity 1, The Counting Principle
Unit 5, Activity 1, The Counting Principle Directions: With a partner find the answer to the following problems. 1. A person buys 3 different shirts (Green, Blue, and Red) and two different pants (Khaki
More informationProbability Review before Quiz. Unit 6 Day 6 Probability
Probability Review before Quiz Unit 6 Day 6 Probability Warm-up: Day 6 1. A committee is to be formed consisting of 1 freshman, 1 sophomore, 2 juniors, and 2 seniors. How many ways can this committee be
More informationQuiz 2 Review - on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II??
Quiz 2 Review - on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II?? Some things to Know, Memorize, AND Understand how to use are n What are the formulas? Pr ncr Fill in the notation
More informationName: Spring P. Walston/A. Moore. Topic worksheet # assigned #completed Teacher s Signature Tree Diagrams FCP
Name: Spring 2016 P. Walston/A. Moore Topic worksheet # assigned #completed Teacher s Signature Tree Diagrams 1-0 13 FCP 1-1 16 Combinations/ Permutations Factorials 1-2 22 1-3 20 Intro to Probability
More informationCOUNTING METHODS. Methods Used for Counting
Ch. 8 COUNTING METHODS From our preliminary work in probability, we often found ourselves wondering how many different scenarios there were in a given situation. In the beginning of that chapter, we merely
More information6) A) both; happy B) neither; not happy C) one; happy D) one; not happy
MATH 00 -- PRACTICE TEST 2 Millersville University, Spring 202 Ron Umble, Instr. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all natural
More informationPermutations and Combinations
Permutations and Combinations In statistics, there are two ways to count or group items. For both permutations and combinations, there are certain requirements that must be met: there can be no repetitions
More informationPermutations and Combinations. Quantitative Aptitude & Business Statistics
Permutations and Combinations Statistics The Fundamental Principle of If there are Multiplication n 1 ways of doing one operation, n 2 ways of doing a second operation, n 3 ways of doing a third operation,
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) 1 6
Math 300 Exam 4 Review (Chapter 11) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Give the probability that the spinner shown would land on
More informationMath 1116 Probability Lecture Monday Wednesday 10:10 11:30
Math 1116 Probability Lecture Monday Wednesday 10:10 11:30 Course Web Page http://www.math.ohio state.edu/~maharry/ Chapter 15 Chances, Probabilities and Odds Objectives To describe an appropriate sample
More informationJUST THE MATHS UNIT NUMBER PROBABILITY 2 (Permutations and combinations) A.J.Hobson
JUST THE MATHS UNIT NUMBER 19.2 PROBABILITY 2 (Permutations and combinations) by A.J.Hobson 19.2.1 Introduction 19.2.2 Rules of permutations and combinations 19.2.3 Permutations of sets with some objects
More informationChapter 11: Probability and Counting Techniques
Chapter 11: Probability and Counting Techniques Diana Pell Section 11.1: The Fundamental Counting Principle Exercise 1. How many different two-letter words (including nonsense words) can be formed when
More information1) If P(E) is the probability that an event will occur, then which of the following is true? (1) 0 P(E) 1 (3) 0 P(E) 1 (2) 0 P(E) 1 (4) 0 P(E) 1
Algebra 2 Review for Unit 14 Test Name: 1) If P(E) is the probability that an event will occur, then which of the following is true? (1) 0 P(E) 1 (3) 0 P(E) 1 (2) 0 P(E) 1 (4) 0 P(E) 1 2) From a standard
More information7 5 Compound Events. March 23, Alg2 7.5B Notes on Monday.notebook
7 5 Compound Events At a juice bottling factory, quality control technicians randomly select bottles and mark them pass or fail. The manager randomly selects the results of 50 tests and organizes the data
More informationSection 11.4: Tree Diagrams, Tables, and Sample Spaces
Section 11.4: Tree Diagrams, Tables, and Sample Spaces Diana Pell Exercise 1. Use a tree diagram to find the sample space for the genders of three children in a family. Exercise 2. (You Try!) A soda machine
More informationProbability Day CIRCULAR PERMUTATIONS
Probability Day 4-11.4 CIRCULAR PERMUTATIONS Ex. 1 How many ways are there to arrange 4 people around a table? (see SmartBoard link) Ex. 2 How many circular permutations are there of: a. V W X Y Z b. M
More informationObjectives: Permutations. Fundamental Counting Principle. Fundamental Counting Principle. Fundamental Counting Principle
and Objectives:! apply fundamental counting principle! compute permutations! compute combinations HL2 Math - Santowski! distinguish permutations vs combinations can be used determine the number of possible
More information, -the of all of a probability experiment. consists of outcomes. (b) List the elements of the event consisting of a number that is greater than 4.
4-1 Sample Spaces and Probability as a general concept can be defined as the chance of an event occurring. In addition to being used in games of chance, probability is used in the fields of,, and forecasting,
More informationACTIVITY 6.7 Selecting and Rearranging Things
ACTIVITY 6.7 SELECTING AND REARRANGING THINGS 757 OBJECTIVES ACTIVITY 6.7 Selecting and Rearranging Things 1. Determine the number of permutations. 2. Determine the number of combinations. 3. Recognize
More informationAlgebra 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)
More information7.1 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
More informationProbability, Permutations, & Combinations LESSON 11.1
Probability, Permutations, & Combinations LESSON 11.1 Objective Define probability Use the counting principle Know the difference between combination and permutation Find probability Probability PROBABILITY:
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Statistics Homework Ch 5 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability
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 informationChapter 5 Probability
Chapter 5 Probability Math150 What s the likelihood of something occurring? Can we answer questions about probabilities using data or experiments? For instance: 1) If my parking meter expires, I will probably
More information5 Elementary Probability Theory
5 Elementary Probability Theory 5.1 What is Probability? The Basics We begin by defining some terms. Random Experiment: any activity with a random (unpredictable) result that can be measured. Trial: one
More informationLAMC Junior Circle January 22, Oleg Gleizer. The Hanoi Tower. Part 2
LAMC Junior Circle January 22, 2012 Oleg Gleizer The Hanoi Tower Part 2 Definition 1 An algorithm is a finite set of clear instructions to solve a problem. An algorithm is called optimal, if the solution
More informationCounting (Enumerative Combinatorics) X. Zhang, Fordham Univ.
Counting (Enumerative Combinatorics) X. Zhang, Fordham Univ. 1 Chance of winning?! What s the chances of winning New York Megamillion Jackpot!! just pick 5 numbers from 1 to 56, plus a mega ball number
More informationThere are three types of mathematicians. Those who can count and those who can t.
1 Counting There are three types of mathematicians. Those who can count and those who can t. 1.1 Orderings The details of the question always matter. So always take a second look at what is being asked
More informationChapter 13 April Vacation Packet
Name: _ Date: Chapter 13 April Vacation Packet Class: _ 1. In a batch of 390 water purifiers, 12 were found to be defective. What is the probability that a water purifier chosen at random will be defective?
More informationSection 5.4 Permutations and Combinations
Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to
More informationMath 12 - Unit 4 Review
Name: Class: Date: Math 12 - Unit 4 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A combination lock opens with the correct three-digit code.
More informationPrecalc Unit 10 Review
Precalc Unit 10 Review Name: Use binomial expansion to expand. 1. 2. 3.. Use binomial expansion to find the term you are asked for. 4. 5 th term of (4x-3y) 8 5. 3 rd term of 6. 4 th term of 7. 2 nd term
More information4.4: The Counting Rules
4.4: The Counting Rules The counting rules can be used to discover the number of possible for a sequence of events. Fundamental Counting Rule In a sequence of n events in which the first one has k 1 possibilities
More informationFinite Math B, Chapter 8 Test Review Name
Finite Math B, Chapter 8 Test Review Name Evaluate the factorial. 1) 6! A) 720 B) 120 C) 360 D) 1440 Evaluate the permutation. 2) P( 10, 5) A) 10 B) 30,240 C) 1 D) 720 3) P( 12, 8) A) 19,958,400 B) C)
More information1111: Linear Algebra I
1111: Linear Algebra I Dr. Vladimir Dotsenko (Vlad) Lecture 7 Dr. Vladimir Dotsenko (Vlad) 1111: Linear Algebra I Lecture 7 1 / 8 Invertible matrices Theorem. 1. An elementary matrix is invertible. 2.
More informationSection 5.4 Permutations and Combinations
Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! = n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to
More informationPermutation. Lesson 5
Permutation Lesson 5 Objective Students will be able to understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound
More information9.5 COUnTIng PRInCIPleS. Using the Addition Principle. learning ObjeCTIveS
800 CHAPTER 9 sequences, ProbAbility ANd counting theory learning ObjeCTIveS In this section, you will: Solve counting problems using the Addition Principle. Solve counting problems using the Multiplication
More informationMATH & STAT Ch.1 Permutations & Combinations JCCSS
THOMAS / 6ch1.doc / P.1 1.1 The Multilication Princile of Counting P.2 If a first oeration can be erformed in n 1 ways, a second oeration in n 2 ways, a third oeration in n 3 ways, and so forth, then the
More informationIn how many ways can a team of three snow sculptors be chosen to represent Amir s school from the nine students who have volunteered?
4.6 Combinations GOAL Solve problems involving combinations. LEARN ABOUT the Math Each year during the Festival du Voyageur, held during February in Winnipeg, Manitoba, high schools compete in the Voyageur
More informationUnit 19 Probability Review
. What is sample space? All possible outcomes Unit 9 Probability Review 9. I can use the Fundamental Counting Principle to count the number of ways an event can happen. 2. What is the difference between
More informationATHS FC Math Department Al Ain Remedial worksheet. Lesson 10.4 (Ellipses)
ATHS FC Math Department Al Ain Remedial worksheet Section Name ID Date Lesson Marks Lesson 10.4 (Ellipses) 10.4, 10.5, 0.4, 0.5 and 0.6 Intervention Plan Page 1 of 19 Gr 12 core c 2 = a 2 b 2 Question
More information6. In how many different ways can you answer 10 multiple-choice questions if each question has five choices?
Pre-Calculus Section 4.1 Multiplication, Addition, and Complement 1. Evaluate each of the following: a. 5! b. 6! c. 7! d. 0! 2. Evaluate each of the following: a. 10! b. 20! 9! 18! 3. In how many different
More information10.2 Theoretical Probability and its Complement
warm-up after 10.1 1. A traveler can choose from 3 airlines, 5 hotels and 4 rental car companies. How many arrangements of these services are possible? 2. Your school yearbook has an editor and assistant
More informationProbability Warm-Up 1 (Skills Review)
Probability Warm-Up 1 (Skills Review) Directions Solve to the best of your ability. (1) Graph the line y = 3x 2. (2) 4 3 = (3) 4 9 + 6 7 = (4) Solve for x: 4 5 x 8 = 12? (5) Solve for x: 4(x 6) 3 = 12?
More informationa) 2, 4, 8, 14, 22, b) 1, 5, 6, 10, 11, c) 3, 9, 21, 39, 63, d) 3, 0, 6, 15, 27, e) 3, 8, 13, 18, 23,
Pre-alculus Midterm Exam Review Name:. Which of the following is an arithmetic sequence?,, 8,,, b),, 6, 0,, c), 9,, 9, 6, d), 0, 6,, 7, e), 8,, 8,,. What is a rule for the nth term of the arithmetic sequence
More informationMAT104: Fundamentals of Mathematics II Summary of Counting Techniques and Probability. Preliminary Concepts, Formulas, and Terminology
MAT104: Fundamentals of Mathematics II Summary of Counting Techniques and Probability Preliminary Concepts, Formulas, and Terminology Meanings of Basic Arithmetic Operations in Mathematics Addition: Generally
More informationChapter 11: Probability and Counting Techniques
Chapter 11: Probability and Counting Techniques Diana Pell Section 11.3: Basic Concepts of Probability Definition 1. A sample space is a set of all possible outcomes of an experiment. Exercise 1. An experiment
More informationCIS 2033 Lecture 6, Spring 2017
CIS 2033 Lecture 6, Spring 2017 Instructor: David Dobor February 2, 2017 In this lecture, we introduce the basic principle of counting, use it to count subsets, permutations, combinations, and partitions,
More informationConcepts. Materials. Objective
. Activity 14 Let Us Count the Ways! Concepts Apply the multiplication counting principle Find the number of permutations in a data set Find the number of combinations in a data set Calculator Skills Factorial:
More informationSTAT Statistics I Midterm Exam One. Good Luck!
STAT 515 - Statistics I Midterm Exam One Name: Instruction: You can use a calculator that has no connection to the Internet. Books, notes, cellphones, and computers are NOT allowed in the test. There are
More informationAlgebra Adventure Directions. Format: Individual or Pairs (works best)
Algebra Adventure Directions Format: Individual or Pairs (works best) Directions: Each student will receive an Algebra Adventure WS that they will keep track of their stations and work. Each pair will
More informationLesson A7 - Counting Techniques and Permutations. Learning Goals:
Learning Goals: * Determine tools and strategies that will determine outcomes more efficiently * Use factorial notation effectively * Determine probabilities for simple ordered events Example 1: You are
More informationPermutations & Combinations
Permutations & Combinations Extension 1 Mathematics HSC Revision UOW PERMUTATIONS AND COMBINATIONS: REVIEW 1. A combination lock has 4 dials each with 10 digits. How many possible arrangements are there?
More informationMATH 2420 Discrete Mathematics Lecture notes
MATH 2420 Discrete Mathematics Lecture notes Series and Sequences Objectives: Introduction. Find the explicit formula for a sequence. 2. Be able to do calculations involving factorial, summation and product
More informationSTATISTICAL COUNTING TECHNIQUES
STATISTICAL COUNTING TECHNIQUES I. Counting Principle The counting principle states that if there are n 1 ways of performing the first experiment, n 2 ways of performing the second experiment, n 3 ways
More informationM146 - Chapter 5 Handouts. Chapter 5
Chapter 5 Objectives of chapter: Understand probability values. Know how to determine probability values. Use rules of counting. Section 5-1 Probability Rules What is probability? It s the of the occurrence
More informationProbability Quiz Review Sections
CP1 Math 2 Unit 9: Probability: Day 7/8 Topic Outline: Probability Quiz Review Sections 5.02-5.04 Name A probability cannot exceed 1. We express probability as a fraction, decimal, or percent. Probabilities
More information13.3 Permutations and Combinations
13.3 Permutations and Combinations There are 6 people who want to use an elevator. There is only room for 4 people. How many ways can 6 people try to fill this elevator (one at a time)? There are 6 people
More informationChapter 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
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 information8.3 Probability with Permutations and Combinations
8.3 Probability with Permutations and Combinations Question 1: How do you find the likelihood of a certain type of license plate? Question 2: How do you find the likelihood of a particular committee? Question
More informationSMML MEET 3 ROUND 1
ROUND 1 1. How many different 3-digit numbers can be formed using the digits 0, 2, 3, 5 and 7 without repetition? 2. There are 120 students in the senior class at Jefferson High. 25 of these seniors participate
More informationHonors Precalculus Chapter 9 Summary Basic Combinatorics
Honors Precalculus Chapter 9 Summary Basic Combinatorics A. Factorial: n! means 0! = Why? B. Counting principle: 1. How many different ways can a license plate be formed a) if 7 letters are used and each
More informationWeek in Review #5 ( , 3.1)
Math 166 Week-in-Review - S. Nite 10/6/2012 Page 1 of 5 Week in Review #5 (2.3-2.4, 3.1) n( E) In general, the probability of an event is P ( E) =. n( S) Distinguishable Permutations Given a set of n objects
More informationFall. Spring. Possible Summer Topics
Fall Paper folding: equilateral triangle (parallel postulate and proofs of theorems that result, similar triangles), Trisect a square paper Divisibility by 2-11 and by combinations of relatively prime
More informationMath 1111 Math Exam Study Guide
Math 1111 Math Exam Study Guide The math exam will cover the mathematical concepts and techniques we ve explored this semester. The exam will not involve any codebreaking, although some questions on the
More informationPERMUTATIONS AND COMBINATIONS
PERMUTATIONS AND COMBINATIONS 1. Fundamental Counting Principle Assignment: Workbook: pg. 375 378 #1-14 2. Permutations and Factorial Notation Assignment: Workbook pg. 382-384 #1-13, pg. 526 of text #22
More information