MATH 166 Exam I Sample Questions. 2. Given the Venn Diagram below, the set (A B) C c consists of which region(s)?
|
|
- Buddy Lee
- 7 years ago
- Views:
Transcription
1 PART I-MULTIPLE CHOICE MATH 166 Exam I Sample Questions 1. Let p be the statement Pi is a rational number. (which is false) and q be the statement 4 is a rational number (which is true). Which of the following is true? (a) p q (b) p q (c) p q (d) p q (e) None of these are true 2. Given the Venn Diagram below, the set (A B) C c consists of which region(s)? (a) b only (b) a, b, c only (c) a, b, c, h only (d) None of these (e) a, b, c, e, h only 3. Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 3, 5, 7}, and B = {1, 3, 5, 7, 9}. Which of the following is A B c? (a) {2} (b) {0, 4, 6, 8} (c) {0, 2, 4, 6, 8} (d) {0, 1, 4, 6, 8, 9} (e) {0, 2, 3, 4, 5, 6, 7, 8} 4. Using the sets in #3 above, let p be the statement {3, 5} A B and q be the statement {2} A. Which of the following is correct? (a) p is true; q is true. (b) p is true; q is false. (c) p is false; q is true. (d) p is false; q is false. (e) None of these
2 5. In the SEC (14 total schools), 8 schools have winning records in Women's Volleyball, 11 schools have winning records in Women's Soccer, and 2 schools do not have winning records in either sport. How many schools have winning records in both sports? (a) 6 (b) 7 (c) None of these (d) 9 (e) Two fair 4-sided dice are rolled. What is the probability that the absolute value of the dierence between the rst and second die is at least one? (For example, if the dice are (1, 3), then 1 3 = 2). (a) 3 5 (b) 5 6 (c) 2 7 (d) 3 4 (e) Two fair 4-sided dice are rolled. What is the probability that at least one of the numbers is a 3? (a) 7 16 (b) 1 8 (c) 1 2 (d) (e) According to the show Guys and Dolls, if a guy is acting strange, It's a probable 12 to 7 that the guy's only doing it for some doll. If these are the odds the man is in love, what is the probability that the man is in love? (a) 7 12 (b) 7 19 (c) 5 12 (d) (e) 5 19
3 9. In a u study of 400 individuals, 145 of them contracted the u. Of those who contracted the u, 60 had been vaccinated, while 190 of those who did not contract the u were vaccinated. If an individual from the study is chosen at random, what is the probability they were vaccinated given they did not contract the u? (a) (b) None of these (c) (d) (e) Given the following: P (A) = 0.2, P (B) = 0.6, P (A c B c ) = 0.2 P (C) = 0.5, P (D) = 0.3, P (C c D c ) = 0.35 Which statement is correct? (a) A and B are mutually exclusive, C and D are independent (b) A and B neither, C and D are independent (c) A and B are neither, C and D are neither (d) A and B are mutually exclusive, C and D are neither (e) A and B are independent, C and D are mutually exclusive 11. Use the tree diagram below to nd P (C): (a) 0.42 (b) 0.9 (c) 0.18 (d) 0.45 (e) None of these 12. Use the tree diagram in #11 to nd P (F C): (a) 3 5 (b) 3 7 (c) (d) None of these 3 (e) 10
4 13. Let U be the set of all MATH 166 students. Let B = {x x is a business major}, M = {x x is male}, and F = {x x is a freshman}. Which of the following describes the set of all MATH 166 students who are male and either not business majors or not freshman or not either one? (a) (M B c ) F c (b) (M B c ) F c (c) M (B c F c ) (d) M (B c F c ) (e) More than one of these is correct. 14. Let p, q, r be the following statements: p : I was in the Corps of Cadets q : I attended a Bonre cut r : I attended all Aggie home football games (a) Write the statement p q r in words. (b) Write the symbolic form of I was in the Corps of Cadets and I have either not attended a Bonre cut or not attended all the Aggie home football games or both.
5 15. (a) (8 pts) Construct a truth table for ( p q) ( p q). (NOTE: Not all columns of the table have to be used) p q T T T F F T F F (b) Is ( p q) ( p q) a contradiction, tautology, or neither? 16. In a campus survey regarding news sources: 4 students use a newspaper, TV, and the Internet for news 20 students use exactly 2 sources for news 14 students use a newspaper for news 43 students do NOT use the Internet for news 13 students use only TV for news 50 students do NOT use TV or a newspaper for news 2 students use only the newspaper and the Internet for news 9 students use TV and a newspaper for news Completely ll in the diagram below and determine how many students participated in the survey (where N = {students who use a newspaper}, T = {students who use TV}, and I = {students who use the Internet}).
6 17. The numbers 1, 2, and 10 are each written on a card and placed in a hat. Two numbers are drawn at the same time, and the product of the numbers is recorded. List the sample space for this experiment. Are the outcomes equally likely? 18. Let S = {s 1, s 2, s 3, s 4, s 5 } be the sample space of an experiment with P (s 1 ) = 0.2, P (s 2 ) = 0.15, and P (s 3 ) = 0.2. (a) If s 4 is twice as likely to occur as s 5, what are their probabilities? (b) If A = {s 1, s 3, s 5 } and B = {s 3, s 4 }, what is P (A B c )? 19. According to the internet (which must be true, right?), 90% of all received is spam. Suppose your spam lter program will correctly mark spam 95% of the time, but also mark legitimate as spam 3% of the time. Given a message is not marked as spam, what is the probability that it really is not spam?
Probability --QUESTIONS-- Principles of Math 12 - Probability Practice Exam 1 www.math12.com
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 informationHomework 20: Compound Probability
Homework 20: Compound Probability Definition The probability of an event is defined to be the ratio of times that you expect the event to occur after many trials: number of equally likely outcomes resulting
More informationEXAM. Exam #3. Math 1430, Spring 2002. April 21, 2001 ANSWERS
EXAM Exam #3 Math 1430, Spring 2002 April 21, 2001 ANSWERS i 60 pts. Problem 1. A city has two newspapers, the Gazette and the Journal. In a survey of 1, 200 residents, 500 read the Journal, 700 read the
More informationComplement. If A is an event, then the complement of A, written A c, means all the possible outcomes that are not in A.
Complement If A is an event, then the complement of A, written A c, means all the possible outcomes that are not in A. For example, if A is the event UNC wins at least 5 football games, then A c is the
More informationContemporary Mathematics- MAT 130. Probability. a) What is the probability of obtaining a number less than 4?
Contemporary Mathematics- MAT 30 Solve the following problems:. A fair die is tossed. What is the probability of obtaining a number less than 4? What is the probability of obtaining a number less than
More informationAP Stats - Probability Review
AP Stats - Probability Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. I toss a penny and observe whether it lands heads up or tails up. Suppose
More informationSection 6.2 Definition of Probability
Section 6.2 Definition of Probability Probability is a measure of the likelihood that an event occurs. For example, if there is a 20% chance of rain tomorrow, that means that the probability that it will
More information2. How many ways can the letters in PHOENIX be rearranged? 7! = 5,040 ways.
Math 142 September 27, 2011 1. How many ways can 9 people be arranged in order? 9! = 362,880 ways 2. How many ways can the letters in PHOENIX be rearranged? 7! = 5,040 ways. 3. The letters in MATH are
More informationMath 210. 1. Compute C(1000,2) (a) 499500. (b) 1000000. (c) 2. (d) 999000. (e) None of the above.
Math 210 1. Compute C(1000,2) (a) 499500. (b) 1000000. (c) 2. (d) 999000. 2. Suppose that 80% of students taking calculus have previously had a trigonometry course. Of those that did, 75% pass their calculus
More information6.042/18.062J Mathematics for Computer Science. Expected Value I
6.42/8.62J Mathematics for Computer Science Srini Devadas and Eric Lehman May 3, 25 Lecture otes Expected Value I The expectation or expected value of a random variable is a single number that tells you
More informationThe overall size of these chance errors is measured by their RMS HALF THE NUMBER OF TOSSES NUMBER OF HEADS MINUS 0 400 800 1200 1600 NUMBER OF TOSSES
INTRODUCTION TO CHANCE VARIABILITY WHAT DOES THE LAW OF AVERAGES SAY? 4 coins were tossed 1600 times each, and the chance error number of heads half the number of tosses was plotted against the number
More informationA probability experiment is a chance process that leads to well-defined outcomes. 3) What is the difference between an outcome and an event?
Ch 4.2 pg.191~(1-10 all), 12 (a, c, e, g), 13, 14, (a, b, c, d, e, h, i, j), 17, 21, 25, 31, 32. 1) What is a probability experiment? A probability experiment is a chance process that leads to well-defined
More informationStatistics 100A Homework 2 Solutions
Statistics Homework Solutions Ryan Rosario Chapter 9. retail establishment accepts either the merican Express or the VIS credit card. total of percent of its customers carry an merican Express card, 6
More informationChapter 6. 1. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace? Ans: 4/52.
Chapter 6 1. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace? 4/52. 2. What is the probability that a randomly selected integer chosen from the first 100 positive
More informationSolutions for Review Problems for Exam 2 Math 1040 1 1. You roll two fair dice. (a) Draw a tree diagram for this experiment.
Solutions for Review Problems for Exam 2 Math 1040 1 1. You roll two fair dice. (a) Draw a tree diagram for this experiment. 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2
More informationA Few Basics of Probability
A Few Basics of Probability Philosophy 57 Spring, 2004 1 Introduction This handout distinguishes between inductive and deductive logic, and then introduces probability, a concept essential to the study
More informationSTAT 319 Probability and Statistics For Engineers PROBABILITY. Engineering College, Hail University, Saudi Arabia
STAT 319 robability and Statistics For Engineers LECTURE 03 ROAILITY Engineering College, Hail University, Saudi Arabia Overview robability is the study of random events. The probability, or chance, that
More informationMath/Stat 394 Homework 2
Math/Stat 39 Homework Due Wednesday Jan 18 1. Six awards are to be given out among 0 students. How many ways can the awards be given out if (a one student will win exactly five awards. (b one student will
More informationProbability and Venn diagrams UNCORRECTED PAGE PROOFS
Probability and Venn diagrams 12 This chapter deals with further ideas in chance. At the end of this chapter you should be able to: identify complementary events and use the sum of probabilities to solve
More informationACMS 10140 Section 02 Elements of Statistics October 28, 2010. Midterm Examination II
ACMS 10140 Section 02 Elements of Statistics October 28, 2010 Midterm Examination II Name DO NOT remove this answer page. DO turn in the entire exam. Make sure that you have all ten (10) pages of the examination
More informationQuestion 1 Formatted: Formatted: Formatted: Formatted:
In many situations in life, we are presented with opportunities to evaluate probabilities of events occurring and make judgments and decisions from this information. In this paper, we will explore four
More informationDefinition and Calculus of Probability
In experiments with multivariate outcome variable, knowledge of the value of one variable may help predict another. For now, the word prediction will mean update the probabilities of events regarding the
More informationLesson 1. Basics of Probability. Principles of Mathematics 12: Explained! www.math12.com 314
Lesson 1 Basics of Probability www.math12.com 314 Sample Spaces: Probability Lesson 1 Part I: Basic Elements of Probability Consider the following situation: A six sided die is rolled The sample space
More information(b) You draw two balls from an urn and track the colors. When you start, it contains three blue balls and one red ball.
Examples for Chapter 3 Probability Math 1040-1 Section 3.1 1. Draw a tree diagram for each of the following situations. State the size of the sample space. (a) You flip a coin three times. (b) You draw
More informationMATH 140 Lab 4: Probability and the Standard Normal Distribution
MATH 140 Lab 4: Probability and the Standard Normal Distribution Problem 1. Flipping a Coin Problem In this problem, we want to simualte the process of flipping a fair coin 1000 times. Note that the outcomes
More informationACMS 10140 Section 02 Elements of Statistics October 28, 2010 Midterm Examination II Answers
ACMS 10140 Section 02 Elements of Statistics October 28, 2010 Midterm Examination II Answers Name DO NOT remove this answer page. DO turn in the entire exam. Make sure that you have all ten (10) pages
More informationPROBABILITY. Chapter. 0009T_c04_133-192.qxd 06/03/03 19:53 Page 133
0009T_c04_133-192.qxd 06/03/03 19:53 Page 133 Chapter 4 PROBABILITY Please stand up in front of the class and give your oral report on describing data using statistical methods. Does this request to speak
More informationFind the indicated probability. 1) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.
Math 0 Practice Test 3 Fall 2009 Covers 7.5, 8.-8.3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. ) If a single
More informationBasic Probability. Probability: The part of Mathematics devoted to quantify uncertainty
AMS 5 PROBABILITY Basic Probability Probability: The part of Mathematics devoted to quantify uncertainty Frequency Theory Bayesian Theory Game: Playing Backgammon. The chance of getting (6,6) is 1/36.
More informationDetermine the empirical probability that a person selected at random from the 1000 surveyed uses Mastercard.
Math 120 Practice Exam II Name You must show work for credit. 1) A pair of fair dice is rolled 50 times and the sum of the dots on the faces is noted. Outcome 2 4 5 6 7 8 9 10 11 12 Frequency 6 8 8 1 5
More information6.3 Conditional Probability and Independence
222 CHAPTER 6. PROBABILITY 6.3 Conditional Probability and Independence Conditional Probability Two cubical dice each have a triangle painted on one side, a circle painted on two sides and a square painted
More informationElementary Statistics and Inference. Elementary Statistics and Inference. 16 The Law of Averages (cont.) 22S:025 or 7P:025.
Elementary Statistics and Inference 22S:025 or 7P:025 Lecture 20 1 Elementary Statistics and Inference 22S:025 or 7P:025 Chapter 16 (cont.) 2 D. Making a Box Model Key Questions regarding box What numbers
More informationProbability, statistics and football Franka Miriam Bru ckler Paris, 2015.
Probability, statistics and football Franka Miriam Bru ckler Paris, 2015 Please read this before starting! Although each activity can be performed by one person only, it is suggested that you work in groups
More informationChapter 13 & 14 - Probability PART
Chapter 13 & 14 - Probability PART IV : PROBABILITY Dr. Joseph Brennan Math 148, BU Dr. Joseph Brennan (Math 148, BU) Chapter 13 & 14 - Probability 1 / 91 Why Should We Learn Probability Theory? Dr. Joseph
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 informationTopic : Probability of a Complement of an Event- Worksheet 1. Do the following:
Topic : Probability of a Complement of an Event- Worksheet 1 1. You roll a die. What is the probability that 2 will not appear 2. Two 6-sided dice are rolled. What is the 3. Ray and Shan are playing football.
More informationHoover High School Math League. Counting and Probability
Hoover High School Math League Counting and Probability Problems. At a sandwich shop there are 2 kinds of bread, 5 kinds of cold cuts, 3 kinds of cheese, and 2 kinds of dressing. How many different sandwiches
More informationCh. 13.2: Mathematical Expectation
Ch. 13.2: Mathematical Expectation Random Variables Very often, we are interested in sample spaces in which the outcomes are distinct real numbers. For example, in the experiment of rolling two dice, we
More informationChapter 5 A Survey of Probability Concepts
Chapter 5 A Survey of Probability Concepts True/False 1. Based on a classical approach, the probability of an event is defined as the number of favorable outcomes divided by the total number of possible
More informationCh. 13.3: More about Probability
Ch. 13.3: More about Probability Complementary Probabilities Given any event, E, of some sample space, U, of a random experiment, we can always talk about the complement, E, of that event: this is the
More informationMath 370, Actuarial Problemsolving Spring 2008 A.J. Hildebrand. Problem Set 1 (with solutions)
Math 370, Actuarial Problemsolving Spring 2008 A.J. Hildebrand Problem Set 1 (with solutions) About this problem set: These are problems from Course 1/P actuarial exams that I have collected over the years,
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups
More information2. Three dice are tossed. Find the probability of a) a sum of 4; or b) a sum greater than 4 (may use complement)
Probability Homework Section P4 1. A two-person committee is chosen at random from a group of four men and three women. Find the probability that the committee contains at least one man. 2. Three dice
More informationIntroductory Probability. MATH 107: Finite Mathematics University of Louisville. March 5, 2014
Introductory Probability MATH 07: Finite Mathematics University of Louisville March 5, 204 What is probability? Counting and probability 2 / 3 Probability in our daily lives We see chances, odds, and probabilities
More informationProbability. a number between 0 and 1 that indicates how likely it is that a specific event or set of events will occur.
Probability Probability Simple experiment Sample space Sample point, or elementary event Event, or event class Mutually exclusive outcomes Independent events a number between 0 and 1 that indicates how
More informationContemporary Mathematics Online Math 1030 Sample Exam I Chapters 12-14 No Time Limit No Scratch Paper Calculator Allowed: Scientific
Contemporary Mathematics Online Math 1030 Sample Exam I Chapters 12-14 No Time Limit No Scratch Paper Calculator Allowed: Scientific Name: The point value of each problem is in the left-hand margin. You
More informationMathematical goals. Starting points. Materials required. Time needed
Level S2 of challenge: B/C S2 Mathematical goals Starting points Materials required Time needed Evaluating probability statements To help learners to: discuss and clarify some common misconceptions about
More informationExam 3 Review/WIR 9 These problems will be started in class on April 7 and continued on April 8 at the WIR.
Exam 3 Review/WIR 9 These problems will be started in class on April 7 and continued on April 8 at the WIR. 1. Urn A contains 6 white marbles and 4 red marbles. Urn B contains 3 red marbles and two white
More informationProbability: Terminology and Examples Class 2, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Probability: Terminology and Examples Class 2, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Know the definitions of sample space, event and probability function. 2. Be able to
More informationMATH 1108 R07 MIDTERM EXAM 1 SOLUTION
MATH 1108 R07 MIDTERM EXAM 1 SOLUTION FALL 2015 - MOON Write your answer neatly and show steps. Except calculators, any electronic devices including laptops and cell phones are not allowed. Do not use
More informationFeb 7 Homework Solutions Math 151, Winter 2012. Chapter 4 Problems (pages 172-179)
Feb 7 Homework Solutions Math 151, Winter 2012 Chapter Problems (pages 172-179) Problem 3 Three dice are rolled. By assuming that each of the 6 3 216 possible outcomes is equally likely, find the probabilities
More informationThe Calculus of Probability
The Calculus of Probability Let A and B be events in a sample space S. Partition rule: P(A) = P(A B) + P(A B ) Example: Roll a pair of fair dice P(Total of 10) = P(Total of 10 and double) + P(Total of
More informationMind on Statistics. Chapter 10
Mind on Statistics Chapter 10 Section 10.1 Questions 1 to 4: Some statistical procedures move from population to sample; some move from sample to population. For each of the following procedures, determine
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 1
Math 370/408, Spring 2008 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 1 About this problem set: These are problems from Course 1/P actuarial exams that I have collected over the years, grouped
More informationFind an expected value involving two events. Find an expected value involving multiple events. Use expected value to make investment decisions.
374 Chapter 8 The Mathematics of Likelihood 8.3 Expected Value Find an expected value involving two events. Find an expected value involving multiple events. Use expected value to make investment decisions.
More informationChapter 4: Probability and Counting Rules
Chapter 4: Probability and Counting Rules Learning Objectives Upon successful completion of Chapter 4, you will be able to: Determine sample spaces and find the probability of an event using classical
More informationM 1313 Review Test 4 1
M 1313 Review Test 4 1 Review for test 4: 1. Let E and F be two events of an experiment, P (E) =. 3 and P (F) =. 2, and P (E F) =.35. Find the following probabilities: a. P(E F) b. P(E c F) c. P (E F)
More informationExam Style Questions. Revision for this topic. Name: Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser
Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. Read each question carefully before you begin answering
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Practice Test Chapter 9 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the odds. ) Two dice are rolled. What are the odds against a sum
More information1) The table lists the smoking habits of a group of college students. Answer: 0.218
FINAL EXAM REVIEW Name ) The table lists the smoking habits of a group of college students. Sex Non-smoker Regular Smoker Heavy Smoker Total Man 5 52 5 92 Woman 8 2 2 220 Total 22 2 If a student is chosen
More informationStat 20: Intro to Probability and Statistics
Stat 20: Intro to Probability and Statistics Lecture 16: More Box Models Tessa L. Childers-Day UC Berkeley 22 July 2014 By the end of this lecture... You will be able to: Determine what we expect the sum
More informationQuestion of the Day. Key Concepts. Vocabulary. Mathematical Ideas. QuestionofDay
QuestionofDay Question of the Day What is the probability that in a family with two children, both are boys? What is the probability that in a family with two children, both are boys, if we already know
More informationStatistics 100A Homework 3 Solutions
Chapter Statistics 00A Homework Solutions Ryan Rosario. Two balls are chosen randomly from an urn containing 8 white, black, and orange balls. Suppose that we win $ for each black ball selected and we
More informationJoint Exam 1/P Sample Exam 1
Joint Exam 1/P Sample Exam 1 Take this practice exam under strict exam conditions: Set a timer for 3 hours; Do not stop the timer for restroom breaks; Do not look at your notes. If you believe a question
More informationSample Term Test 2A. 1. A variable X has a distribution which is described by the density curve shown below:
Sample Term Test 2A 1. A variable X has a distribution which is described by the density curve shown below: What proportion of values of X fall between 1 and 6? (A) 0.550 (B) 0.575 (C) 0.600 (D) 0.625
More informationProbability, Statistics, & Data Analysis (PSD) Numbers: Concepts & Properties (NCP) 400 600
Name ACT Prep PSD/NCP Probability, Statistics, & Data Analysis (PSD) Numbers: Concepts & Properties (NCP) 400 600 Table of Contents: PSD 40: Calculate the missing data value, given the average and all
More informationDecision Making Under Uncertainty. Professor Peter Cramton Economics 300
Decision Making Under Uncertainty Professor Peter Cramton Economics 300 Uncertainty Consumers and firms are usually uncertain about the payoffs from their choices Example 1: A farmer chooses to cultivate
More informationLecture 13. Understanding Probability and Long-Term Expectations
Lecture 13 Understanding Probability and Long-Term Expectations Thinking Challenge What s the probability of getting a head on the toss of a single fair coin? Use a scale from 0 (no way) to 1 (sure thing).
More informationSAT Math Facts & Formulas Review Quiz
Test your knowledge of SAT math facts, formulas, and vocabulary with the following quiz. Some questions are more challenging, just like a few of the questions that you ll encounter on the SAT; these questions
More informationSTATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4
STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate
More informationThat s Not Fair! ASSESSMENT #HSMA20. Benchmark Grades: 9-12
That s Not Fair! ASSESSMENT # Benchmark Grades: 9-12 Summary: Students consider the difference between fair and unfair games, using probability to analyze games. The probability will be used to find ways
More informationNo Solution Equations Let s look at the following equation: 2 +3=2 +7
5.4 Solving Equations with Infinite or No Solutions So far we have looked at equations where there is exactly one solution. It is possible to have more than solution in other types of equations that are
More informationProbability Using Dice
Using Dice One Page Overview By Robert B. Brown, The Ohio State University Topics: Levels:, Statistics Grades 5 8 Problem: What are the probabilities of rolling various sums with two dice? How can you
More information6th Grade Lesson Plan: Probably Probability
6th Grade Lesson Plan: Probably Probability Overview This series of lessons was designed to meet the needs of gifted children for extension beyond the standard curriculum with the greatest ease of use
More informationGrade 6 Math Circles March 2, 2011 Counting
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 6 Math Circles March 2, 2011 Counting Venn Diagrams Example 1: Ms. Daly surveyed her class of 26
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam 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 that the result
More informationChapter 4 Lecture Notes
Chapter 4 Lecture Notes Random Variables October 27, 2015 1 Section 4.1 Random Variables A random variable is typically a real-valued function defined on the sample space of some experiment. For instance,
More informationProbability. Sample space: all the possible outcomes of a probability experiment, i.e., the population of outcomes
Probability Basic Concepts: Probability experiment: process that leads to welldefined results, called outcomes Outcome: result of a single trial of a probability experiment (a datum) Sample space: all
More informationCurriculum Design for Mathematic Lesson Probability
Curriculum Design for Mathematic Lesson Probability This curriculum design is for the 8th grade students who are going to learn Probability and trying to show the easiest way for them to go into this class.
More informationWeek 2: Conditional Probability and Bayes formula
Week 2: Conditional Probability and Bayes formula We ask the following question: suppose we know that a certain event B has occurred. How does this impact the probability of some other A. This question
More informationLab 11. Simulations. The Concept
Lab 11 Simulations In this lab you ll learn how to create simulations to provide approximate answers to probability questions. We ll make use of a particular kind of structure, called a box model, that
More informationBasic Probability Theory II
RECAP Basic Probability heory II Dr. om Ilvento FREC 408 We said the approach to establishing probabilities for events is to Define the experiment List the sample points Assign probabilities to the sample
More informationPROBABILITY SECOND EDITION
PROBABILITY SECOND EDITION Table of Contents How to Use This Series........................................... v Foreword..................................................... vi Basics 1. Probability All
More informationStatistics 100A Homework 1 Solutions
Chapter 1 tatistics 100A Homework 1 olutions Ryan Rosario 1. (a) How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers? The first two
More information2.5 Conditional Probabilities and 2-Way Tables
2.5 Conditional Probabilities and 2-Way Tables Learning Objectives Understand how to calculate conditional probabilities Understand how to calculate probabilities using a contingency or 2-way table It
More informationSolutions to Homework 6 Statistics 302 Professor Larget
s to Homework 6 Statistics 302 Professor Larget Textbook Exercises 5.29 (Graded for Completeness) What Proportion Have College Degrees? According to the US Census Bureau, about 27.5% of US adults over
More information10-4-10 Year 9 mathematics: holiday revision. 2 How many nines are there in fifty-four?
DAY 1 Mental questions 1 Multiply seven by seven. 49 2 How many nines are there in fifty-four? 54 9 = 6 6 3 What number should you add to negative three to get the answer five? 8 4 Add two point five to
More informationBayesian Tutorial (Sheet Updated 20 March)
Bayesian Tutorial (Sheet Updated 20 March) Practice Questions (for discussing in Class) Week starting 21 March 2016 1. What is the probability that the total of two dice will be greater than 8, given that
More informationHandout #1: Mathematical Reasoning
Math 101 Rumbos Spring 2010 1 Handout #1: Mathematical Reasoning 1 Propositional Logic A proposition is a mathematical statement that it is either true or false; that is, a statement whose certainty or
More informationSet operations and Venn Diagrams. COPYRIGHT 2006 by LAVON B. PAGE
Set operations and Venn Diagrams Set operations and Venn diagrams! = { x x " and x " } This is the intersection of and. # = { x x " or x " } This is the union of and. n element of! belongs to both and,
More informationStatistics 2014 Scoring Guidelines
AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home
More informationMA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.
MA 5 Lecture 4 - Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the
More informationFACTORS, PRIME NUMBERS, H.C.F. AND L.C.M.
Mathematics Revision Guides Factors, Prime Numbers, H.C.F. and L.C.M. Page 1 of 16 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier FACTORS, PRIME NUMBERS, H.C.F. AND L.C.M. Version:
More informationMath 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2
Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable
More informationSTAT 35A HW2 Solutions
STAT 35A HW2 Solutions http://www.stat.ucla.edu/~dinov/courses_students.dir/09/spring/stat35.dir 1. A computer consulting firm presently has bids out on three projects. Let A i = { awarded project i },
More informationECON1003: Analysis of Economic Data Fall 2003 Answers to Quiz #2 11:40a.m. 12:25p.m. (45 minutes) Tuesday, October 28, 2003
ECON1003: Analysis of Economic Data Fall 2003 Answers to Quiz #2 11:40a.m. 12:25p.m. (45 minutes) Tuesday, October 28, 2003 1. (4 points) The number of claims for missing baggage for a well-known airline
More informationUnit 19: Probability Models
Unit 19: Probability Models Summary of Video Probability is the language of uncertainty. Using statistics, we can better predict the outcomes of random phenomena over the long term from the very complex,
More informationMath 166 - Week in Review #4. A proposition, or statement, is a declarative sentence that can be classified as either true or false, but not both.
Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166 - Week in Review #4 Sections A.1 and A.2 - Propositions, Connectives, and Truth Tables A proposition, or statement, is a declarative sentence that
More informationGraphs and charts - quiz
Level A 1. In a tally chart, what number does this represent? A) 2 B) 4 C) 8 D) 10 2. In a pictogram if represents 2 people, then how many people do these symbols represent? A) 3 people B) 5 people C)
More informationCOUNTING SUBSETS OF A SET: COMBINATIONS
COUNTING SUBSETS OF A SET: COMBINATIONS DEFINITION 1: Let n, r be nonnegative integers with r n. An r-combination of a set of n elements is a subset of r of the n elements. EXAMPLE 1: Let S {a, b, c, d}.
More information