# Review for Test 2. Chapters 4, 5 and 6

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Review for Test 2 Chapters 4, 5 and 6 1. You roll a fair six-sided die. Find the probability of each event: a. Event A: rolling a 3 1/6 b. Event B: rolling a 7 0 c. Event C: rolling a number less than 5 4/6 d. Event D: rolling an odd number 3/6 e. Event E: rolling a 1 or a 6 2/6 f. Event F: rolling a number that is at least 4 3/6 2. You roll two fair six-sided dice. Find the probability for each event: a. Event A: the difference of the two number is 3 6/36 b. Event B: the difference of the two numbers is 0 6/36 c. Event C: the sum of the two numbers is less than 6 10/36 d. Event D: the sum of the two numbers is an even number 18/36 e. Event E: the sum of the two numbers is not a 5 32/36 f. Event F: the sum of the two numbers is at least 4 33/36 g. Event G: the sum is 4 or getting doubles 3/36+6/36-1/36 = 8/36 h. Event H: the sum is 7 or getting doubles 6/36+6/36 = 12/36 3. Identify the sample space for each probability experiment: a. guessing the last digit in a telephone number S = {0,1,2,3,4,5,6,7,8,9} b. determining a person s blood type (A, B, AB, O) and Rh-factor (positive, negative) S = {A+, A-, B+,B-, AB+, AB-, O+, O-} c. the gender of three children S = {GGG, GGB, GBG, BGG, GBB, BGB, BBG, BBB} 1

2 4. The M&Ms milk chocolate candies have six colors: brown, blue, red, orange, yellow and green. The distribution of the colors are shown in the table below: Color brown blue red orange yellow green Probability 13% 24% 13% 20% 14% a. What is the probability that a randomly selected candy is green? Explain. 16% because the probabilities must add up to 1. b. What is the probability that a randomly selected candy is either red or orange? 13%+20% = 33% c. What is the probability that a randomly selected candy is not blue? = 0.76 = 76% d. What is the probability that a randomly selected candy is neither brown nor green? 24% + 13% +20% +14% =71% 5. In a local school, 40% carry a backpack, and 50% carry a wallet. 10% of the students carry both a backpack and a wallet. If a student is selected at random, find the probability that the student carries a backpack or a wallet. P(B or W) =P(B) +P(W) P(B and W) = = What is the probability that three randomly selected persons have a birthday on the 1 st of any months? (12/365)*(12/365) = Are these pairs of events mutually exclusive (disjoint)? a. has ridden a roller coaster; has ridden a Ferris wheel No, they are not disjoint; it is possible that someone has ridden a roller coaster and a Ferris wheel b. owns a classical music CD; owns a jazz CD No, they are not disjoint; it is possible that someone owns a classical music CD and a jazz CD c. is a senior; is a junior These events are disjoint. Someone cannot be a senior and a junior. d. has brown hair; has brown eyes No, they are not disjoint; it is possible that someone has brown hair and brown eyes. e. is left-handed; is right-handed This is arguable, but I would say these events are disjoint; someone cannot be left-handed and right-handed. But you can argue about this, because there are some people who have no hand preference. In that case they are not disjoint events. f. has shoulder-length hair; is male No, they are not disjoint; it is possible that someone has shoulder-length hair and is a male. g. rolling doubles with a pair of dice; rolling a sum of 8 No, they are not disjoint. It is possible to roll doubles with a pair of dice and the sum of the two numbers is 8. (that would be 4 and 4 double and the sum is 8) h. rolling a 3 on one die; rolling a sum of 10 2

3 These are disjoint. With a regular die it is impossible to roll a 3 with one die and in the same time the sum of the two numbers is 10. (that would require the second die to show a 7, which is impossible with a regular 6-sided die) 8. Decide whether the events are independent or dependent: a. a salmon swims successfully through a dam (A) and another salmon swims successfully through the same dam (B) These events are independent. The second salmon s success doesn t depend on the first salmon s success. b. tossing a coin and getting a head (A), and then rolling a six-sided die and obtaining a 6 (B) These events are independent. The die s outcome doesn t depend on the outcome of the coin toss. c. driving over 85 miles per hour (A), and then getting in a car accident (B) These events are dependent. You have a higher chance to get in a car accident if you drive over 85 miles per hour. 9. The probability that a salmon swims successfully through a dam is a. find the probability that two salmons successfully swims through the dam Since the salmons successes are independent of each other, the probability is (0.85)(0.85) = b. find the probability that three salmons successfully swims through the dam (0.85)(0.85)(0.85)= c. find the probability that none of the three salmons is successful (1-0.85)(1-0.85)(1-0.85) = The table shows the estimated number (in thousands) of earned degrees conferred in the year of 2000 by level and gender. Level of degree Gender Male Female Total Associate Bachelor Master Doctor Total A person who earned a degree in 2000 is randomly selected. Find the probability of selecting someone who a. earned a bachelor s degree 1161/2152 b. earned a master s degree 414/2152 c. earned a master or doctorate degree. (414+46)/2152 d. earned a bachelor or associate degree. ( )/2152 e. earned an associate degree and the person is a female. 323/2152 3

4 f. earned a doctorate degree and the person is a male. 27/2152 g. earned a doctorate degree given that the person is a male. 27/924 h. is a female given that the person earned a master degree. 227/414 i. is a male given that the person earned a doctorate degree. 27/46 j. earned a bachelor degree given that the person is a female. 659/ A company that makes cartons finds The probability of producing a carton with a puncture is 0.05 The probability that a carton has a smashed corner is The probability that a carton has a puncture and has a smashed corner is a. What do you think: Are the events selecting a carton with a puncture and selecting a carton with smashed corner independent? Explain. Having a smashed corner should not depend on whether the carton had a puncture or not, so these events should be independent. One way to check it using the given probabilities: If P(A)P(B) = P(A and B), then the events are independent. Here we have : (0.05)(0.08) which is 0.004, which is P(A and B), so the events are independent. b. If a quality inspector randomly selects a carton, find the probability that the carton has a puncture or has a smashed corner. P(A or B) = P(A)+P(B)-P(A and B) = = A doctor gives a patient a 60% chance of surviving bypass surgery after a heart attack. If the patient survives the surgery, he has a 50% chance that the heart damage will heal. Find the probability that the patient survives and the heart damage heals. Let BS be the event that the patient survives bypass surgery. Let H be the event that the heart damage will heal. Then P(BS) = 0.60, and also we have a conditional probability: GIVEN that the patient survives, the probability that the heart damage will heal is 0.5, that is P(H BS) = 0.5 We want to know P(BS and H). Using the formula of the conditional probability: P(H and BS) = P(H BS) P(BS) = (0.6)(0.5) = 0.3 That is the probability that the patient survives and the heart damage heals is 30%. 13. Forty-three race cars started the 2004 Daytona 500. How many ways can the cars finish first, second, and third? Since order DOES matter for the medals, it s permutation. 43 P 3 = How many ways can you arrange the letters of MATHEMATICS? 4

5 11! ! 2! 2! = 15. A state s department of transportation plans to develop a new section of interstate highway and receives 16 bids for the project. The state plans to hire four of the bidding companies. How many ways can the state hire the four companies? Since order does NOT matter here, it s combination. 16 C 4 = A survey asked a sample of people how many vehicles each owns. The random variable X represents the number of vehicles owned. x P(x) a. Verify that the distribution is a probability distribution. It is. All the probabilities are between 0 and 1, and the probabilities add up to 1. b. Find the mean of the distribution. Mean: c. Find the variance and the standard deviation of the distribution. Standard deviation: % adults say that they have trouble sleeping at night. You randomly select five adults and ask each if he or she has trouble sleeping at night. a. Decide whether the experiment is a binomial experiment. It is. The number of trials is fixed (n=5), the probability for each is the same (p=0.6), the trials are independent, and there are only two outcomes, Success: trouble sleeping, and Failure: no trouble sleeping b. Construct a binomial distribution. X P(X) c. Graph the distribution. 5

7 b. What is the probability that the mean gasoline (87) price of 18 randomly selected gas stations is more than \$3.25? We can t answer to this one. We don t know anything about the population distribution, and 18 is not big enough to use the CLT. c. What is the probability that the mean gasoline (87) price of 38 randomly selected gas stations is between \$3.20 and \$3.22? Now we can calculate the probability because n >30. We can find the two z-scores with mean 3.19 and s.d. = = Answer: According to Harper's magazine, in the U.S. the time children spend watching television per year follows a normal distribution with mean of 1500 hours and a standard deviation of 250 hours. a. What percent of children watch television for less than 1200 hours per year? Draw the distribution, shade in the area that represents the percentage, and find its value b. Solve the appropriate equation and fill in the blank: 10% of all children watch more than _ hours of television per year. c. Imagine that all possible random samples of size 25 are taken from the population of U.S. children, and then the means from each sample are graphed to form the sampling distribution of sample means. Using the Central Limit Theorem determine the shape, center, and standard deviation of the distribution, and draw the sampling distribution showing the mean and the standard deviation. Shape: normal since the population distribution is normal Mean: same as the population mean = 1500 hours S.D. = 250 = d. What s the probability that the mean number of hours per year that 25 randomly selected children watch television is more than 1600 hours? e. What s the probability that the mean number of hours per year that 25 randomly selected children watch television is less than 1390 hours?

### Chapter 4 Probability

The Big Picture of Statistics Chapter 4 Probability Section 4-2: Fundamentals Section 4-3: Addition Rule Sections 4-4, 4-5: Multiplication Rule Section 4-7: Counting (next time) 2 What is probability?

### MAT 1000. Mathematics in Today's World

MAT 1000 Mathematics in Today's World We talked about Cryptography Last Time We will talk about probability. Today There are four rules that govern probabilities. One good way to analyze simple probabilities

### AP 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

### Construct and Interpret Binomial Distributions

CH 6.2 Distribution.notebook A random variable is a variable whose values are determined by the outcome of the experiment. 1 CH 6.2 Distribution.notebook A probability distribution is a function which

### Probability: The Study of Randomness Randomness and Probability Models. IPS Chapters 4 Sections 4.1 4.2

Probability: The Study of Randomness Randomness and Probability Models IPS Chapters 4 Sections 4.1 4.2 Chapter 4 Overview Key Concepts Random Experiment/Process Sample Space Events Probability Models Probability

### Ch5: Discrete Probability Distributions Section 5-1: Probability Distribution

Recall: Ch5: Discrete Probability Distributions Section 5-1: Probability Distribution A variable is a characteristic or attribute that can assume different values. o Various letters of the alphabet (e.g.

### MULTIPLE 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

### Section 6.2 ~ Basics of Probability. Introduction to Probability and Statistics SPRING 2016

Section 6.2 ~ Basics of Probability Introduction to Probability and Statistics SPRING 2016 Objective After this section you will know how to find probabilities using theoretical and relative frequency

### Key Concept. Properties

MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 6 Normal Probability Distributions 6 1 Review and Preview 6 2 The Standard Normal Distribution 6 3 Applications of Normal

### The number of phone calls to the attendance office of a high school on any given school day A) continuous B) discrete

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) State whether the variable is discrete or continuous.

### Sample 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

### I. WHAT IS PROBABILITY?

C HAPTER 3 PROBABILITY Random Experiments I. WHAT IS PROBABILITY? The weatherman on 0 o clock news program states that there is a 20% chance that it will snow tomorrow, a 65% chance that it will rain and

### Characteristics of Binomial Distributions

Lesson2 Characteristics of Binomial Distributions In the last lesson, you constructed several binomial distributions, observed their shapes, and estimated their means and standard deviations. In Investigation

### Tree Diagrams. on time. The man. by subway. From above tree diagram, we can get

1 Tree Diagrams Example: A man takes either a bus or the subway to work with probabilities 0.3 and 0.7, respectively. When he takes the bus, he is late 30% of the days. When he takes the subway, he is

### PROBABILITY 14.3. section. The Probability of an Event

4.3 Probability (4-3) 727 4.3 PROBABILITY In this section In the two preceding sections we were concerned with counting the number of different outcomes to an experiment. We now use those counting techniques

### According to the Book of Odds, the probability that a randomly selected U.S. adult usually eats breakfast is 0.61.

Probability Law of large numbers: if we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single number. Probability: probability

### Sample Questions for Mastery #5

Name: Class: Date: Sample Questions for Mastery #5 Multiple Choice Identify the choice that best completes the statement or answers the question.. For which of the following binomial experiments could

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 0.4987 B) 0.9987 C) 0.0010 D) 0.

Ch. 5 Normal Probability Distributions 5.1 Introduction to Normal Distributions and the Standard Normal Distribution 1 Find Areas Under the Standard Normal Curve 1) Find the area under the standard normal

### Chapter 6 Random Variables

Chapter 6 Random Variables Day 1: 6.1 Discrete Random Variables Read 340-344 What is a random variable? Give some examples. A numerical variable that describes the outcomes of a chance process. Examples:

### Review the following from Chapter 5

Bluman, Chapter 6 1 Review the following from Chapter 5 A surgical procedure has an 85% chance of success and a doctor performs the procedure on 10 patients, find the following: a) The probability that

### Section 6-5 Sample Spaces and Probability

492 6 SEQUENCES, SERIES, AND PROBABILITY 52. How many committees of 4 people are possible from a group of 9 people if (A) There are no restrictions? (B) Both Juan and Mary must be on the committee? (C)

### MULTIPLE 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

### The Binomial Probability Distribution

The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Objectives After this lesson we will be able to: determine whether a probability

### What is the probability of throwing a fair die and receiving a six? Introduction to Probability. Basic Concepts

Basic Concepts Introduction to Probability A probability experiment is any experiment whose outcomes relies purely on chance (e.g. throwing a die). It has several possible outcomes, collectively called

### Math 150 Sample Exam #2

Problem 1. (16 points) TRUE or FALSE. a. 3 die are rolled, there are 1 possible outcomes. b. If two events are complementary, then they are mutually exclusive events. c. If A and B are two independent

### The basics of probability theory. Distribution of variables, some important distributions

The basics of probability theory. Distribution of variables, some important distributions 1 Random experiment The outcome is not determined uniquely by the considered conditions. For example, tossing a

### Statistical Inference. Prof. Kate Calder. If the coin is fair (chance of heads = chance of tails) then

Probability Statistical Inference Question: How often would this method give the correct answer if I used it many times? Answer: Use laws of probability. 1 Example: Tossing a coin If the coin is fair (chance

### 2. 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

### Chapter 4: Probabilities and Proportions

Stats 11 (Fall 2004) Lecture Note Introduction to Statistical Methods for Business and Economics Instructor: Hongquan Xu Chapter 4: Probabilities and Proportions Section 4.1 Introduction In the real world,

### Question: What is the probability that a five-card poker hand contains a flush, that is, five cards of the same suit?

ECS20 Discrete Mathematics Quarter: Spring 2007 Instructor: John Steinberger Assistant: Sophie Engle (prepared by Sophie Engle) Homework 8 Hints Due Wednesday June 6 th 2007 Section 6.1 #16 What is the

### Worked examples Basic Concepts of Probability Theory

Worked examples Basic Concepts of Probability Theory Example 1 A regular tetrahedron is a body that has four faces and, if is tossed, the probability that it lands on any face is 1/4. Suppose that one

### Unit 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,

### Stats Review Chapters 5-6

Stats Review Chapters 5-6 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

Chapter 3 Probability 2012 Pearson Education, Inc. All rights reserved. 1 of 20 Chapter Outline 3.1 Basic Concepts of Probability 3.2 Conditional Probability and the Multiplication Rule 3.3 The Addition

### Section 6.1 Discrete Random variables Probability Distribution

Section 6.1 Discrete Random variables Probability Distribution Definitions a) Random variable is a variable whose values are determined by chance. b) Discrete Probability distribution consists of the values

### PROBABILITY. Chapter Overview

Chapter 6 PROBABILITY 6. Overview Probability is defined as a quantitative measure of uncertainty a numerical value that conveys the strength of our belief in the occurrence of an event. The probability

### AP * Statistics Review. Probability

AP * Statistics Review Probability Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production of,

### MATH 10: Elementary Statistics and Probability Chapter 3: Probability Topics

MATH 10: Elementary Statistics and Probability Chapter 3: Probability Topics Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides, you should

### ACMS 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

### Definition 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

### Section Tree Diagrams. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 12.5 Tree Diagrams What You Will Learn Counting Principle Tree Diagrams 12.5-2 Counting Principle If a first experiment can be performed in M distinct ways and a second experiment can be performed

### 33 Probability: Some Basic Terms

33 Probability: Some Basic Terms In this and the coming sections we discuss the fundamental concepts of probability at a level at which no previous exposure to the topic is assumed. Probability has been

### MATHEMATICS FOR ENGINEERS STATISTICS TUTORIAL 4 PROBABILITY DISTRIBUTIONS

MATHEMATICS FOR ENGINEERS STATISTICS TUTORIAL 4 PROBABILITY DISTRIBUTIONS CONTENTS Sample Space Accumulative Probability Probability Distributions Binomial Distribution Normal Distribution Poisson Distribution

### Chapter 14 From Randomness to Probability

Chapter 14 From Randomness to Probability 199 Chapter 14 From Randomness to Probability 1. Sample spaces. a) S = { HH, HT, TH, TT} All of the outcomes are equally likely to occur. b) S = { 0, 1, 2, 3}

### Basic Probability Theory I

A Probability puzzler!! Basic Probability Theory I Dr. Tom Ilvento FREC 408 Our Strategy with Probability Generally, we want to get to an inference from a sample to a population. In this case the population

### Counting principle, permutations, combinations, probabilities

Counting Methods Counting principle, permutations, combinations, probabilities Part 1: The Fundamental Counting Principle The Fundamental Counting Principle is the idea that if we have a ways of doing

### Chapter 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

### Probability. 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

### STT 315 Practice Problems I for Sections

STT 35 Practice Problems I for Sections. - 3.7. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. ) Parking at a university has become

### Lecture 1 Introduction Properties of Probability Methods of Enumeration Asrat Temesgen Stockholm University

Lecture 1 Introduction Properties of Probability Methods of Enumeration Asrat Temesgen Stockholm University 1 Chapter 1 Probability 1.1 Basic Concepts In the study of statistics, we consider experiments

### STAT 145 (Notes) Al Nosedal Department of Mathematics and Statistics University of New Mexico. Fall

STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico Fall 2013 CHAPTER 10 INTRODUCING PROBABILITY. Randomness and Probability We call a phenomenon

### Chapter 1 Axioms of Probability. Wen-Guey Tzeng Computer Science Department National Chiao University

Chapter 1 Axioms of Probability Wen-Guey Tzeng Computer Science Department National Chiao University Introduction Luca Paccioli(1445-1514), Studies of chances of events Niccolo Tartaglia(1499-1557) Girolamo

### CHAPTER 7: THE CENTRAL LIMIT THEOREM

CHAPTER 7: THE CENTRAL LIMIT THEOREM Exercise 1. Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews

### DETERMINE whether the conditions for a binomial setting are met. COMPUTE and INTERPRET probabilities involving binomial random variables

1 Section 7.B Learning Objectives After this section, you should be able to DETERMINE whether the conditions for a binomial setting are met COMPUTE and INTERPRET probabilities involving binomial random

### A 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

### Section 5-3 Binomial Probability Distributions

Section 5-3 Binomial Probability Distributions Key Concept This section presents a basic definition of a binomial distribution along with notation, and methods for finding probability values. Binomial

### Chapter 6: Random Variables

Chapter : Random Variables Section.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter Random Variables.1 Discrete and Continuous Random Variables.2 Transforming and Combining

### c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?

### Topic 6: Conditional Probability and Independence

Topic 6: September 15-20, 2011 One of the most important concepts in the theory of probability is based on the question: How do we modify the probability of an event in light of the fact that something

### Probability 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

### A-Level Maths. in a week. Core Maths - Co-ordinate Geometry of Circles. Generating and manipulating graph equations of circles.

A-Level Maths in a week Core Maths - Co-ordinate Geometry of Circles Generating and manipulating graph equations of circles. Statistics - Binomial Distribution Developing a key tool for calculating probability

### Probability & Probability Distributions

Probability & Probability Distributions Carolyn J. Anderson EdPsych 580 Fall 2005 Probability & Probability Distributions p. 1/61 Probability & Probability Distributions Elementary Probability Theory Definitions

### Homework 5 Solutions

Math 130 Assignment Chapter 18: 6, 10, 38 Chapter 19: 4, 6, 8, 10, 14, 16, 40 Chapter 20: 2, 4, 9 Chapter 18 Homework 5 Solutions 18.6] M&M s. The candy company claims that 10% of the M&M s it produces

### STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS

STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS 1. If two events (both with probability greater than 0) are mutually exclusive, then: A. They also must be independent. B. They also could

### Probability: The Study of Randomness Randomness and Probability Models

Probability: The Study of Randomness Randomness and Probability Models IPS Chapters 4.1 and 4.2 2009 W.H. Freeman and Company Objectives (IPS Chapters 4.1 and 4.2) Randomness and Probability models Probability

### Chapter 6 ATE: Random Variables Alternate Examples and Activities

Probability Chapter 6 ATE: Random Variables Alternate Examples and Activities [Page 343] Alternate Example: NHL Goals In 2010, there were 1319 games played in the National Hockey League s regular season.

### Statistics 100 Binomial and Normal Random Variables

Statistics 100 Binomial and Normal Random Variables Three different random variables with common characteristics: 1. Flip a fair coin 10 times. Let X = number of heads out of 10 flips. 2. Poll a random

### Chapter 5: Normal Probability Distributions - Solutions

Chapter 5: Normal Probability Distributions - Solutions Note: All areas and z-scores are approximate. Your answers may vary slightly. 5.2 Normal Distributions: Finding Probabilities If you are given that

### Lesson 1: Experimental and Theoretical Probability

Lesson 1: Experimental and Theoretical Probability Probability is the study of randomness. For instance, weather is random. In probability, the goal is to determine the chances of certain events happening.

### Activity- The Energy Choices Game

Activity- The Energy Choices Game Purpose Energy is a critical resource that is used in all aspects of our daily lives. The world s supply of nonrenewable resources is limited and our continued use of

### Lesson 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

### Statistics 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

### . Notice that this means P( A B )

Probability II onditional Probability You already know probabilities change when more information is known. For example the probability of getting type I diabetes for the general population is.06. The

### Conditional Probability and General Multiplication Rule

Conditional Probability and General Multiplication Rule Objectives: - Identify Independent and dependent events - Find Probability of independent events - Find Probability of dependent events - Find Conditional

### Probability Review. ICPSR Applied Bayesian Modeling

Probability Review ICPSR Applied Bayesian Modeling Random Variables Flip a coin. Will it be heads or tails? The outcome of a single event is random, or unpredictable What if we flip a coin 10 times? How

### Probability. A random sample is selected in such a way that every different sample of size n has an equal chance of selection.

1 3.1 Sample Spaces and Tree Diagrams Probability This section introduces terminology and some techniques which will eventually lead us to the basic concept of the probability of an event. The Rare Event

### Mind on Statistics. Chapter 8

Mind on Statistics Chapter 8 Sections 8.1-8.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable

### Thursday, November 13: 6.1 Discrete Random Variables

Thursday, November 13: 6.1 Discrete Random Variables Read 347 350 What is a random variable? Give some examples. What is a probability distribution? What is a discrete random variable? Give some examples.

### AP Stats Fall Final Review Ch. 5, 6

AP Stats Fall Final Review 2015 - Ch. 5, 6 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

Chance deals with the concepts of randomness and the use of probability as a measure of how likely it is that particular events will occur. A National Statement on Mathematics for Australian Schools, 1991

### 94 Counting Solutions for Chapter 3. Section 3.2

94 Counting 3.11 Solutions for Chapter 3 Section 3.2 1. Consider lists made from the letters T, H, E, O, R, Y, with repetition allowed. (a How many length-4 lists are there? Answer: 6 6 6 6 = 1296. (b

### Lesson Plans for (9 th Grade Main Lesson) Possibility & Probability (including Permutations and Combinations)

Lesson Plans for (9 th Grade Main Lesson) Possibility & Probability (including Permutations and Combinations) Note: At my school, there is only room for one math main lesson block in ninth grade. Therefore,

### Name: Date: Use the following to answer questions 2-4:

Name: Date: 1. A phenomenon is observed many, many times under identical conditions. The proportion of times a particular event A occurs is recorded. What does this proportion represent? A) The probability

### Unit 21: Binomial Distributions

Unit 21: Binomial Distributions Summary of Video In Unit 20, we learned that in the world of random phenomena, probability models provide us with a list of all possible outcomes and probabilities for how

### Chapter 3 Probability

Chapter 3 Probability We have completed our study of Descriptive Statistics and are headed for Statistical Inference. Before we get there, we need to learn a little bit about probability. 3.1 Basic Concepts

### Notes 3 Autumn Independence. Two events A and B are said to be independent if

MAS 108 Probability I Notes 3 Autumn 2005 Independence Two events A and B are said to be independent if P(A B) = P(A) P(B). This is the definition of independence of events. If you are asked in an exam

### ACMS 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

### Cork Institute of Technology. CIT Mathematics Examination, Paper 2 Sample Paper A

Cork Institute of Technology CIT Mathematics Examination, 2015 Paper 2 Sample Paper A Answer ALL FIVE questions. Each question is worth 20 marks. Total marks available: 100 marks. The standard Formulae

### + Section 6.2 and 6.3

Section 6.2 and 6.3 Learning Objectives After this section, you should be able to DEFINE and APPLY basic rules of probability CONSTRUCT Venn diagrams and DETERMINE probabilities DETERMINE probabilities

### Chapter 5 - Probability

Chapter 5 - Probability 5.1 Basic Ideas An experiment is a process that, when performed, results in exactly one of many observations. These observations are called the outcomes of the experiment. The set

### Exam 2 Study Guide and Review Problems

Exam 2 Study Guide and Review Problems Exam 2 covers chapters 4, 5, and 6. You are allowed to bring one 3x5 note card, front and back, and your graphing calculator. Study tips: Do the review problems below.

### E3: PROBABILITY AND STATISTICS lecture notes

E3: PROBABILITY AND STATISTICS lecture notes 2 Contents 1 PROBABILITY THEORY 7 1.1 Experiments and random events............................ 7 1.2 Certain event. Impossible event............................

### Contemporary 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

### AP Statistics 7!3! 6!

Lesson 6-4 Introduction to Binomial Distributions Factorials 3!= Definition: n! = n( n 1)( n 2)...(3)(2)(1), n 0 Note: 0! = 1 (by definition) Ex. #1 Evaluate: a) 5! b) 3!(4!) c) 7!3! 6! d) 22! 21! 20!

### Section 5 Part 2. Probability Distributions for Discrete Random Variables

Section 5 Part 2 Probability Distributions for Discrete Random Variables Review and Overview So far we ve covered the following probability and probability distribution topics Probability rules Probability

### Chapter 15. Definitions: experiment: is the act of making an observation or taking a measurement.

MATH 11008: Probability Chapter 15 Definitions: experiment: is the act of making an observation or taking a measurement. outcome: one of the possible things that can occur as a result of an experiment.

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

STATISTICS/GRACEY PRACTICE TEST/EXAM 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the given random variable as being discrete or continuous.