Math-Essentials. Lesson 9-2: Counting Combinations
|
|
- Jewel McBride
- 5 years ago
- Views:
Transcription
1 Math-Essentials Lesson 9-2: Counting Combinations
2 Vocabulary Permutation: The number of ways a group of items can be arranged in order without reusing items.
3 Permutations What if you don t want to arrange all of the items? Instead you want to pick from a group of items but arrange only a portion of them. How many ways are there to do this? For example: Sean s band has 10 original songs. The recording company will only accept 6 songs on a demo CD. How many different ways can you choose 6 of the 10 and then arrange them on the demo disk? We call this a permutation of n items taken r at a time. 10P For Sean s CD: 10 permutate 6 n P r 6
4 Permutations. If we were making a permutation using the letters D, A, W, and G DAWG and WADG would be two distinct words. ORDER MATTERS!! (with permutations) a different order of members is a different group all together!! Permutation if arranging 4 items, pick any 4 items. Rearrange those 4 into a different order. If this new arrangement can be counted as a separate arrangement, it is a permutation.
5 I have 4 bills in my wallet: $1, $2, $5, $10 How many different sequences of bills can I take out of my wallet, if I only take 3 out? P ways 1, 2, 5 1, 5, 2 2, 1, 5 2, 5, 1 5, 1, 2 5, 2, 1 10, 2, 1 10, 1, 2 2, 10, 1 2, 1, 10 1, 10, 2 1, 2, 10 1, 10, 5 1, 5, 10 10, 1, 5 10, 5, 1 5, 1, 10 5, 10, 1 10, 2, 5 10, 5, 2 2, 10, 5 2, 5, 10 5, 10, 2 5, 2, 10 Each of these groups is just a permutation of the # of ways to arrange 3 different bills.
6 I have 4 bills in my wallet: $1, $2, $5, $10 How many different sums of money can I take out of my wallet, if I only take 3 bills out? 1, 2, 5 1, 5, 2 2, 1, 5 2, 5, 1 5, 1, 2 5, 2, 1 10, 2, 1 10, 1, 2 2, 10, 1 2, 1, 10 1, 10, 2 1, 2, 10 1, 10, 5 1, 5, 10 10, 1, 5 10, 5, 1 5, 1, 10 5, 10, 1 10, 2, 5 10, 5, 2 2, 10, 5 2, 5, 10 5, 10, 2 5, 2, 10 = $8 = $13 = $16 = $17 4 ways ORDER Doesn t MATTER!! a different order of pulling the same 3 bills out doesn t make a different sum. If order doesn t matter, then we have double counted the number of sums by the number of ways to arrange 3 different bills in order.
7 We call this new method of counting a combination. 1, 2, 5 1, 5, 2 2, 1, 5 2, 5, 1 5, 1, 2 5, 2, 1 10, 2, 1 10, 1, 2 2, 10, 1 2, 1, 10 1, 10, 2 1, 2, 10 P 3! n! Cr r! r!( n r)! n Pr n 1, 10, 5 1, 5, 10 10, 1, 5 10, 5, 1 5, 1, 10 5, 10, 1 10, 2, 5 10, 5, 2 2, 10, 5 2, 5, 10 5, 10, 2 5, 2, 10 = $8 = $13 = $16 = $ Using the multiplication principle of counting we must divide out the number of ways we have double counted.
8 Order Matters vs. Order Doesn t Matter Different order separate items n items taken r at a time Different Order not separate items must divide out the double counting n choose r items The symbol for this is: Permutation n! n P r ( n r)! n n C r P r n! r! r!( n r)! Combination n! r!( n r)!
9 Your turn: Permutation Combination You are tasked to count the number of ways the following items could occur. Decide if you will use a permutation or a combination (write P or C ) for each of the following: 3 people chosen out of a group of 10 to be the president, vice president and secretary of a club. 3 people chosen out of a group of 10 to members of a committee. The top 3 finishers of a race involving 20 runners. The 1 st, 2 nd, and 3 rd place finishers of a race involving 20 runners.
10 Key Question about Order Do I care if an item comes first or last (or somewhere in between) in the group of items I select? If you care about where/when the item is picked, order matters (use permutations) If not, order does not matter (use combinations)
11 Counting the # of ways to arrange choices: Order matters vs. Order Doesn t matter. ORDER MATTERS!! (with permutations) a different order of members is a different group all together!! Order matters: golf and flog are different words using the same 4 letter. Order doesn t matter: when summing a roll of two dice, getting a 3 first and a 5 second is the same as getting a 5 first and a 3 second. Since the order of rolling dice doesn t matter when finding the sum of the two dice we call this a combination.
12 Order Matters vs. Order Doesn t Matter Permutation Different order of the same items counted as a separate arrangement Different ways to line up people/things in order If you see the words in order in the question Different presidencies Different prizes based upon order of finish in a race
13 Order Matters vs. Order Doesn t Matter Combination Different order of the same items can not be counted as separate arrangement Different total scores Different total amounts of money Different hands of cards dealt in a game of cards (in games where you can rearrange the cards in your hand once they are dealt) Different committees of people
14 Combination: n C r n! r!( n r)! You are paying a for groceries at the store. You have the following bills: $100, $50, $20, $10, $5, $2, and $1. What are number of different sums of money that you can pull out of your if you pull out 3 bills without looking? 7 C 3 7! 3!(7 3)! 7! 3!(4)! 7*6*5*4! 35 3!(4)!
15 Combinations using your calculator n! 10! n C r 10C5 10 choose 5 r!( n r)! 5!(10 5)! Clear your screen Math button Scroll to PRB then enter 10 Select option 3 then hit 5 Now enter
16 C r n! Your turn: n r!( n r)! 7 choose 2 items =? 21 13C2? 78
17 Your turn: How many different committees with 5 members can be formed when choosing from 25 candidates? You are dealt 5 cards in a card game where you are allowed to rearrange the cards in your hand. How many different 5 card hands are possible? (you may rearrange the cards after they have been dealt). The number of ways 700 people can line up while in the lunch line.
18 Permutations or Combinations? Your turn: How many different ways can the 1 st, 2 nd, and 3 rd place trophies can be awarded to the top three contestants of 100 entrants. How many different 5 card hands can be dealt from a pack of 52 cards. (in this game you are not allowed to rearrange your cards in your hand after they have been dealt). You are shooting arrows at a target. Each ring on the target is worth a certain number of points. Your score is determined by the sum of points earned by shooting 3 arrows. How many different scores are possible using 3 arrows? (assume all 3 hit the target and you may hit the same ring more than once).
19 A Crash Course on Playing Cards for the Digital Age The group of cards that a player is given is called a hand 52 cards in a deck 2 colors: red ( ) and black ( ) 26 cards of each color 4 suits: Hearts, Diamonds, Spades, Clubs 13 cards in each suit 3 face cards: Jack, Queen, and King 10 numbered cards: 1 through 10 The 1 card is called an Ace 2 extra cards called the Jokers are sometimes added to the deck (making it a 54 card deck)
20 What did we learn? 1. The difference between discrete and continuous data. 2. The multiplication rule for counting ways things can be arranged in order. 3. The difference between a permutation and a combination when counting the ways to arrange things in order. 4. How to use a calculator to find the number of ways to arrange thing in order (permutation or combination).
Math 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 information{ a, b }, { a, c }, { b, c }
12 d.) 0(5.5) c.) 0(5,0) h.) 0(7,1) a.) 0(6,3) 3.) Simplify the following combinations. PROBLEMS: C(n,k)= the number of combinations of n distinct objects taken k at a time is COMBINATION RULE It can easily
More informationClassical vs. Empirical Probability Activity
Name: Date: Hour : Classical vs. Empirical Probability Activity (100 Formative Points) For this activity, you will be taking part in 5 different probability experiments: Rolling dice, drawing cards, drawing
More informationActivity 1: Play comparison games involving fractions, decimals and/or integers.
Students will be able to: Lesson Fractions, Decimals, Percents and Integers. Play comparison games involving fractions, decimals and/or integers,. Complete percent increase and decrease problems, and.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More 9.-9.3 Practice Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. ) In how many ways can you answer the questions on
More informationPoker Hands. Christopher Hayes
Poker Hands Christopher Hayes Poker Hands The normal playing card deck of 52 cards is called the French deck. The French deck actually came from Egypt in the 1300 s and was already present in the Middle
More informationPrinciples of Mathematics 12: Explained!
www.math12.com 284 Lesson 2, Part One: Basic Combinations Basic combinations: In the previous lesson, when using the fundamental counting principal or permutations, the order of items to be arranged mattered.
More informationOH! THE MATH THAT THEY'LL KNOW
Box Cars and One-Eyed Jacks OH! THE MATH THAT THEY'LL KNOW JANE FELLING CCTCA 2016 jane@boxcarsandoneeyedjacks.com phone 1-866-342-3386 / 1-780-440-6284 boxcarsandoneeyedjacks.com fax 1-780-440-1619 BoxCarsEduc
More informationPoker: Further Issues in Probability. Poker I 1/29
Poker: Further Issues in Probability Poker I 1/29 How to Succeed at Poker (3 easy steps) 1 Learn how to calculate complex probabilities and/or memorize lots and lots of poker-related probabilities. 2 Take
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 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 informationMath Games Played with Cards and Dice (K-3)
Math Games Played with Cards and Dice (K-3) Copyright 2009, IPMG Publishing IPMG Publishing 18362 Erin Bay Eden Prairie, Minnesota 55347 phone: (612) 802-9090 www.iplaymathgames.com ISBN 978-1-934218-08-2
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 information(a) Suppose you flip a coin and roll a die. Are the events obtain a head and roll a 5 dependent or independent events?
Unit 6 Probability Name: Date: Hour: Multiplication Rule of Probability By the end of this lesson, you will be able to Understand Independence Use the Multiplication Rule for independent events Independent
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 informationMore Probability: Poker Hands and some issues in Counting
More Probability: Poker Hands and some issues in Counting Data From Thursday Everybody flipped a pair of coins and recorded how many times they got two heads, two tails, or one of each. We saw that the
More informationCounting 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
More information1) = 10) 4-15 = 2) (-4)(-3) = 11) = 4) -9 6 = 13) = 5) = 14) (-3)(15) = = 15) 7) = 16) -7 (-18) =
Name: Ms. Napolitano Date: Activity # Day 10 : I can use integer operations to solve real world problems. Try Now (10) Add, Subtract, Multiply or Divide. 1) -80-4 = 10) 4-15 = 2) (-4)(-3) = 11) 16 33 =
More informationProbability MAT230. Fall Discrete Mathematics. MAT230 (Discrete Math) Probability Fall / 37
Probability MAT230 Discrete Mathematics Fall 2018 MAT230 (Discrete Math) Probability Fall 2018 1 / 37 Outline 1 Discrete Probability 2 Sum and Product Rules for Probability 3 Expected Value MAT230 (Discrete
More informationTABLE OF CONTENTS. Introduction 1. How To Use This Book 3. Using Games As A Teaching Strategy 5. Math Journal Masters 7.
TABLE OF CONTENTS Introduction 1 How To Use This Book 3 Using Games As A Teaching Strategy 5 Math Journal Masters 7 Math Backpacks 11 Materials 15 SHUFFLING INTO MATH WITH THESE INTRODUCTORY CARD GAMES
More informationPan (7:30am) Juan (8:30am) Juan (9:30am) Allison (10:30am) Allison (11:30am) Mike L. (12:30pm) Mike C. (1:30pm) Grant (2:30pm)
STAT 225 FALL 2012 EXAM ONE NAME Your Section (circle one): Pan (7:30am) Juan (8:30am) Juan (9:30am) Allison (10:30am) Allison (11:30am) Mike L. (12:30pm) Mike C. (1:30pm) Grant (2:30pm) Grant (3:30pm)
More informationFoundations 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
More informationUp & Down GOAL OF THE GAME UP&DOWN CARD A GAME BY JENS MERKL & JEAN-CLAUDE PELLIN ART BY CAMILLE CHAUSSY
Up & Down A GAME BY JENS MERKL & JEAN-CLAUDE PELLIN ART BY CAMILLE CHAUSSY GOAL OF THE GAME UP&DOWN is a trick taking game with plenty of ups and downs. This is because prior to each trick, one of the
More information1. An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building?
1. An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building? 2. A particular brand of shirt comes in 12 colors, has a male version and a female version,
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 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 informationThis 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
More informationUNIT 9B Randomness in Computa5on: Games with Random Numbers Principles of Compu5ng, Carnegie Mellon University - CORTINA
UNIT 9B Randomness in Computa5on: Games with Random Numbers 1 Rolling a die from random import randint def roll(): return randint(0,15110) % 6 + 1 OR def roll(): return randint(1,6) 2 1 Another die def
More informationProbability Simulation User s Manual
Probability Simulation User s Manual Documentation of features and usage for Probability Simulation Copyright 2000 Corey Taylor and Rusty Wagner 1 Table of Contents 1. General Setup 3 2. Coin Section 4
More informationChapter 2 Integers. Math 20 Activity Packet Page 1
Chapter 2 Integers Contents Chapter 2 Integers... 1 Introduction to Integers... 3 Adding Integers with Context... 5 Adding Integers Practice Game... 7 Subtracting Integers with Context... 9 Mixed Addition
More informationThe student will explain and evaluate the financial impact and consequences of gambling.
What Are the Odds? Standard 12 The student will explain and evaluate the financial impact and consequences of gambling. Lesson Objectives Recognize gambling as a form of risk. Calculate the probabilities
More informationConditional Probability Worksheet
Conditional Probability Worksheet P( A and B) P(A B) = P( B) Exercises 3-6, compute the conditional probabilities P( AB) and P( B A ) 3. P A = 0.7, P B = 0.4, P A B = 0.25 4. P A = 0.45, P B = 0.8, P A
More informationMATH 215 DISCRETE MATHEMATICS INSTRUCTOR: P. WENG
MATH DISCRETE MATHEMATICS INSTRUCTOR: P. WENG Counting and Probability Suggested Problems Basic Counting Skills, Inclusion-Exclusion, and Complement. (a An office building contains 7 floors and has 7 offices
More informationMath 12 Academic Assignment 9: Probability Outcomes: B8, G1, G2, G3, G4, G7, G8
Math 12 Academic Assignment 9: Probability Outcomes: B8, G1, G2, G3, G4, G7, G8 Name: 45 1. A customer chooses 5 or 6 tapes from a bin of 40. What is the expression that gives the total number of possibilities?
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 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 informationLET S PLAY PONTOON. Pontoon also offers many unique payouts as well as a Super Bonus of up to $5000 on certain hands.
How to play PONTOON LET S PLAY PONTOON Pontoon is a popular game often played in homes around Australia. Pontoon is great fun on its own or as an introduction to other more strategic casino card games
More informationCSE 21: Midterm 1 Solution
CSE 21: Midterm 1 Solution August 16, 2007 No books, no calculators. Two double-sided 3x5 cards with handwritten notes allowed. Before starting the test, please write your test number on the top-right
More informationPROBLEM SET 2 Due: Friday, September 28. Reading: CLRS Chapter 5 & Appendix C; CLR Sections 6.1, 6.2, 6.3, & 6.6;
CS231 Algorithms Handout #8 Prof Lyn Turbak September 21, 2001 Wellesley College PROBLEM SET 2 Due: Friday, September 28 Reading: CLRS Chapter 5 & Appendix C; CLR Sections 6.1, 6.2, 6.3, & 6.6; Suggested
More information2.5 Sample Spaces Having Equally Likely Outcomes
Sample Spaces Having Equally Likely Outcomes 3 Sample Spaces Having Equally Likely Outcomes Recall that we had a simple example (fair dice) before on equally-likely sample spaces Since they will appear
More informationMaking 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
More informationConditional Probability Worksheet
Conditional Probability Worksheet EXAMPLE 4. Drug Testing and Conditional Probability Suppose that a company claims it has a test that is 95% effective in determining whether an athlete is using a steroid.
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 informationApril 10, ex) Draw a tree diagram of this situation.
April 10, 2014 12-1 Fundamental Counting Principle & Multiplying Probabilities 1. Outcome - the result of a single trial. 2. Sample Space - the set of all possible outcomes 3. Independent Events - when
More informationActivity 6: Playing Elevens
Activity 6: Playing Elevens Introduction: In this activity, the game Elevens will be explained, and you will play an interactive version of the game. Exploration: The solitaire game of Elevens uses a deck
More informationVenn Diagram Problems
Venn Diagram Problems 1. In a mums & toddlers group, 15 mums have a daughter, 12 mums have a son. a) Julia says 15 + 12 = 27 so there must be 27 mums altogether. Explain why she could be wrong: b) There
More informationCombat Air Patrol. Kevin White. (This article was originally published in Lone Warrior 187)
Combat Air Patrol Kevin White (This article was originally published in Lone Warrior 187) This is a WW2 air and naval game inspired by the Carrier campaigns in the Pacific. Situation Somewhere in the Pacific
More informationDeveloped by Rashmi Kathuria. She can be reached at
Developed by Rashmi Kathuria. She can be reached at . Photocopiable Activity 1: Step by step Topic Nature of task Content coverage Learning objectives Task Duration Arithmetic
More informationProbability Homework Pack 1
Dice 2 Probability Homework Pack 1 Probability Investigation: SKUNK In the game of SKUNK, we will roll 2 regular 6-sided dice. Players receive an amount of points equal to the total of the two dice, unless
More informationPermutations: The number of arrangements of n objects taken r at a time is. P (n, r) = n (n 1) (n r + 1) =
Section 6.6: Mixed Counting Problems We have studied a number of counting principles and techniques since the beginning of the course and when we tackle a counting problem, we may have to use one or a
More informationDiscrete Finite Probability Probability 1
Discrete Finite Probability Probability 1 In these notes, I will consider only the finite discrete case. That is, in every situation the possible outcomes are all distinct cases, which can be modeled by
More informationIndividual 5 th Grade
Individual 5 th Grade Instructions: Problems 1 10 are multiple choice and count towards your team score. Bubble in the letter on your answer sheet. Be sure to erase all mistakes completely. 1. Which one
More informationIntroduction. Firstly however we must look at the Fundamental Principle of Counting (sometimes referred to as the multiplication rule) which states:
Worksheet 4.11 Counting Section 1 Introduction When looking at situations involving counting it is often not practical to count things individually. Instead techniques have been developed to help us count
More information10 Game. Chapter. The PV Unit comes with two built-in games for your enjoyment. The games are named Game-1 and Game-2.
Chapter 10 Game The PV Unit comes with two built-in games for your enjoyment. The games are named Game-1 and Game-2. Entering the Game Mode and Selecting a Game... 130 Game-1... 130 How to play... 131
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 informationAcing Math (One Deck At A Time!): A Collection of Math Games. Table of Contents
Table of Contents Introduction to Acing Math page 5 Card Sort (Grades K - 3) page 8 Greater or Less Than (Grades K - 3) page 9 Number Battle (Grades K - 3) page 10 Place Value Number Battle (Grades 1-6)
More informationMaking 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.
More informationProbability of Independent Events. If A and B are independent events, then the probability that both A and B occur is: P(A and B) 5 P(A) p P(B)
10.5 a.1, a.5 TEKS Find Probabilities of Independent and Dependent Events Before You found probabilities of compound events. Now You will examine independent and dependent events. Why? So you can formulate
More informationPermutations. Used when "ORDER MATTERS"
Date: Permutations Used when "ORDER MATTERS" Objective: Evaluate expressions involving factorials. (AN6) Determine the number of possible arrangements (permutations) of a list of items. (AN8) 1) Mrs. Hendrix,
More informationThe point value of each problem is in the left-hand margin. You must show your work to receive any credit, except on problems 1 & 2. Work neatly.
Introduction to Statistics Math 1040 Sample Exam II Chapters 5-7 4 Problem Pages 4 Formula/Table Pages Time Limit: 90 Minutes 1 No Scratch Paper Calculator Allowed: Scientific Name: The point value of
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 information9.1 Counting Principle and Permutations
9.1 Counting Principle and Permutations A sporting goods store offers 3 types of snowboards (all-mountain, freestyle, carving) and 2 types of boots (soft or hybrid). How many choices are there for snowboarding
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 informationMaths games and activities to help your child s learning Enjoy!
Maths games and activities to help your child s learning Enjoy! DICE GAMES Dice games are fun! They are also one of the oldest of all kinds of games: there are records of dice being played over 5,000 years
More informationDescribe the variable as Categorical or Quantitative. If quantitative, is it discrete or continuous?
MATH 2311 Test Review 1 7 multiple choice questions, worth 56 points. (Test 1) 3 free response questions, worth 44 points. (Test 1 FR) Terms and Vocabulary; Sample vs. Population Discrete vs. Continuous
More informationBRIDGE is a card game for four players, who sit down at a
THE TRICKS OF THE TRADE 1 Thetricksofthetrade In this section you will learn how tricks are won. It is essential reading for anyone who has not played a trick-taking game such as Euchre, Whist or Five
More informationNwheatleyschaller s The Next Step...Conditional Probability
CK-12 FOUNDATION Nwheatleyschaller s The Next Step...Conditional Probability Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) Meery To access a customizable version of
More informationIntermediate Math Circles November 1, 2017 Probability I
Intermediate Math Circles November 1, 2017 Probability I Probability is the study of uncertain events or outcomes. Games of chance that involve rolling dice or dealing cards are one obvious area of application.
More informationWhatcom County Math Championship 2017 Probability + Statistics 4 th Grade
Probability + Statistics 4 th Grade 1. nya has two spinners, with each space the same area. If she adds the result of both spinners, what is the probability that her answer will be even? Write the answer
More informationChapter 3: PROBABILITY
Chapter 3 Math 3201 1 3.1 Exploring Probability: P(event) = Chapter 3: PROBABILITY number of outcomes favourable to the event total number of outcomes in the sample space An event is any collection of
More informationGames for Drill and Practice
Frequent practice is necessary to attain strong mental arithmetic skills and reflexes. Although drill focused narrowly on rote practice with operations has its place, Everyday Mathematics also encourages
More informationCorners! How To Play - a Comprehensive Guide. Written by Peter V. Costescu RPClasses.com
Corners! How To Play - a Comprehensive Guide. Written by Peter V. Costescu 2017 RPClasses.com How to Play Corners A Comprehensive Guide There are many different card games out there, and there are a variety
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 informationSuch a description is the basis for a probability model. Here is the basic vocabulary we use.
5.2.1 Probability Models When we toss a coin, we can t know the outcome in advance. What do we know? We are willing to say that the outcome will be either heads or tails. We believe that each of these
More informationAlgebra II Probability and Statistics
Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Slide 3 / 241 Table of Contents click on the topic to go to that section Sets Independence and Conditional Probability
More informationDomino Games. Variation - This came can also be played by multiplying each side of a domino.
Domino Games Domino War This is a game for two people. 1. Place all the dominoes face down. 2. Each person places their hand on a domino. 3. At the same time, flip the domino over and whisper the sum of
More informationGAMBLING ( ) Name: Partners: everyone else in the class
Name: Partners: everyone else in the class GAMBLING Games of chance, such as those using dice and cards, oporate according to the laws of statistics: the most probable roll is the one to bet on, and the
More informationCounting Poker Hands
Counting Poker Hands George Ballinger In a standard deck of cards there are kinds of cards: ce (),,,,,,,,,, ack (), ueen () and ing (). Each of these kinds comes in four suits: Spade (), Heart (), Diamond
More informationCOMPOUND 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)
More informationProbability & Expectation. Professor Kevin Gold
Probability & Expectation Professor Kevin Gold Review of Probability so Far (1) Probabilities are numbers in the range [0,1] that describe how certain we should be of events If outcomes are equally likely
More informationAlgebra II. Sets. Slide 1 / 241 Slide 2 / 241. Slide 4 / 241. Slide 3 / 241. Slide 6 / 241. Slide 5 / 241. Probability and Statistics
Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Slide 3 / 241 Slide 4 / 241 Table of Contents click on the topic to go to that section Sets Independence and Conditional
More informationPermutations and Combinations Practice Test
Name: Class: Date: Permutations and Combinations Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Suppose that license plates in the fictional
More informationAlgebra II. Slide 1 / 241. Slide 2 / 241. Slide 3 / 241. Probability and Statistics. Table of Contents click on the topic to go to that section
Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 241 Sets Independence and Conditional Probability
More informationTest 2 SOLUTIONS (Chapters 5 7)
Test 2 SOLUTIONS (Chapters 5 7) 10 1. I have been sitting at my desk rolling a six-sided die (singular of dice), and counting how many times I rolled a 6. For example, after my first roll, I had rolled
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 informationConvert the Egyptian numeral to Hindu-Arabic form. 1) A) 3067 B) 3670 C) 3607 D) 367
MATH 100 -- PRACTICE EXAM 2 Millersville University, Spring 2011 Ron Umble, Instr. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the Egyptian
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 informationABE/ASE Standards Mathematics
[Lesson Title] TEACHER NAME PROGRAM NAME Program Information Playing the Odds [Unit Title] Data Analysis and Probability NRS EFL(s) 3 4 TIME FRAME 240 minutes (double lesson) ABE/ASE Standards Mathematics
More informationHere are two situations involving chance:
Obstacle Courses 1. Introduction. Here are two situations involving chance: (i) Someone rolls a die three times. (People usually roll dice in pairs, so dice is more common than die, the singular form.)
More informationBridge Players: 4 Type: Trick-Taking Card rank: A K Q J Suit rank: NT (No Trumps) > (Spades) > (Hearts) > (Diamonds) > (Clubs)
Bridge Players: 4 Type: Trick-Taking Card rank: A K Q J 10 9 8 7 6 5 4 3 2 Suit rank: NT (No Trumps) > (Spades) > (Hearts) > (Diamonds) > (Clubs) Objective Following an auction players score points by
More informationSuppose you are supposed to select and carry out oneof a collection of N tasks, and there are T K different ways to carry out task K.
Addition Rule Counting 1 Suppose you are supposed to select and carry out oneof a collection of N tasks, and there are T K different ways to carry out task K. Then the number of different ways to select
More informationLEARN HOW TO PLAY MINI-BRIDGE
MINI BRIDGE - WINTER 2016 - WEEK 1 LAST REVISED ON JANUARY 29, 2016 COPYRIGHT 2016 BY DAVID L. MARCH INTRODUCTION THE PLAYERS MiniBridge is a game for four players divided into two partnerships. The partners
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 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 informationSALES AND MARKETING Department MATHEMATICS. Combinatorics and probabilities. Tutorials and exercises
SALES AND MARKETING Department MATHEMATICS 2 nd Semester Combinatorics and probabilities Tutorials and exercises Online document : http://jff-dut-tc.weebly.com section DUT Maths S2 IUT de Saint-Etienne
More informationPoker: Probabilities of the Various Hands
Poker: Probabilities of the Various Hands 22 February 2012 Poker II 22 February 2012 1/27 Some Review from Monday There are 4 suits and 13 values. The suits are Spades Hearts Diamonds Clubs There are 13
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 informationPermutations and Combinations Section
A B I L E N E C H R I S T I A N U N I V E R S I T Y Department of Mathematics Permutations and Combinations Section 13.3-13.4 Dr. John Ehrke Department of Mathematics Fall 2012 Permutations A permutation
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 informationCMPSCI 240: Reasoning Under Uncertainty First Midterm Exam
CMPSCI 240: Reasoning Under Uncertainty First Midterm Exam February 18, 2015. Name: ID: Instructions: Answer the questions directly on the exam pages. Show all your work for each question. Providing more
More information