Math 150 Sample Exam #2

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Math 150 Sample Exam #2"

Transcription

1 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 events, then P (A and B) = P (A) P (B). d. If a family has three children, the probability that two of them are girls is 3. e. Two dice are rolled, Event A is getting a sum greater than 10, and event B is getting a sum of odd number. Event A and event B are mutually exclusive. f. The arrival time of a student in a classroom 10 minutes after the scheduled beginning time of class is an example of continuous random variable. g. In a binomial experiment, if the probability of success is 0.7, the probability of failure is 0.3. h. A random variable with binomial distribution is a discrete random variable. Problem 2. (12 points) Two die are rolled. a. What is the probability of getting a sum of odd number? b. What is the probability of getting a sum that is at least 2? c. What is the probability of getting a sum that is odd or less than?

2 Problem 3. (20 points) Suppose that two balls are randomly drawn in succession, without replacement, from a box containing 7 red and green balls. a. Complete and label the tree diagram as follows that will describe the probabilities of the various outcomes. Fill your answers in the boxes provided. Red Start Red Green Green Red Green First Draw Second Draw b. Give the following values: P (2 nd Green 1 st Red) = P (1 st Green and 2 nd Red) = c. What is the probability of getting two of different colors?

3 Problem 4. (10 points) Suppose you plan to insure your new laptop computer, which you will be taking to campus, against theft for the amount of $2000. An insurance company claims that their records indicate 0.2% of such computers on college campuses are stolen within one year and offers to insure. If the insurance company wants to maintain expected earnings of $200 per such policy, what should the premium be? Problem 5. (10 points) In a hospital unit, there are 14 nurses and 6 physicians. nurses and 4 physicians are females. Staff Females Males Nurses 6 Physicians 4 2 If a staff person is selected, a. Find the probability that the subject is a nurse or male. b. Find the probability that the subject is female physician. c. If two people are selected without replacement, what is the probability that both are female physicians?

4 Problem 6. (12 points) Determine whether the given table represents a probability distribution for a random variable. State the reasons. A. X P(X) B. X P(X) C. X P(X)

5 Problem 7 (10 points) A ski loses $70,000 per season when it does not snow very much and makes $250,000 in profit when it does snow at lot. The probability of it snowing at least 75 inches (a good season) is 40%. If the random variable X that represents the earnings of the ski resort. A. Find the probability distribution for the random variable X. B. Find the expected values (mean) for the ski resort. Problem ( points) There is a binomial experiment with the following numbers: The fixed number of trial is n = 12; Every trial is independent of any other trial; There are only two possible outcomes for each trial, success (S) or failure (F); The probability of success (S) are the same for all trials, which is p = P(S) = 0.. X : the number of successes, then A. List all the possible values of X : { } B. Set up the probability of X successes if X = 7:

6 Problem 9. (10 points) It is believed that 90% of the people interviewed got the H1N1 vaccine. If 10 people are selected at random, A. Find the probability that exactly 7 people interviewed got the H1N1 vaccine (use the table provided). B. Find the probability that at least 2 people interviewed got the H1N1 vaccine (use the table provided). C. Find the expected number of people interview got the H1N1 vaccine. D. Find the standard deviation of the number of people interview got the H1N1 vaccine.

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

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.

More information

Basic Probability Theory I

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

More information

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

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.

More information

AP * Statistics Review. 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,

More information

Chapter 6 Random Variables

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:

More information

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 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 information

Solutions 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. 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 information

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

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

More information

Stats Review Chapters 5-6

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

More information

. Notice that this means P( A B )

. 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

More information

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

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

More information

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 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 information

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

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

More information

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

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.

More information

Section 6.1 Discrete Random variables Probability Distribution

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

More information

I. WHAT IS PROBABILITY?

I. WHAT IS PROBABILITY? C HAPTER 3 PROAILITY Random Experiments I. WHAT IS PROAILITY? The weatherman on 10 o clock news program states that there is a 20% chance that it will snow tomorrow, a 65% chance that it will rain and

More information

Grade 7/8 Math Circles Fall 2012 Probability

Grade 7/8 Math Circles Fall 2012 Probability 1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 2012 Probability Probability is one of the most prominent uses of mathematics

More information

+ Section 6.2 and 6.3

+ 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

More information

ECON1003: 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 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 information

X: 0 1 2 3 4 5 6 7 8 9 Probability: 0.061 0.154 0.228 0.229 0.173 0.094 0.041 0.015 0.004 0.001

X: 0 1 2 3 4 5 6 7 8 9 Probability: 0.061 0.154 0.228 0.229 0.173 0.094 0.041 0.015 0.004 0.001 Tuesday, January 17: 6.1 Discrete Random Variables Read 341 344 What is a random variable? Give some examples. What is a probability distribution? What is a discrete random variable? Give some examples.

More information

Worked examples Basic Concepts of Probability Theory

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

More information

PROBABILITY 14.3. section. The Probability of an Event

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

More information

Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 4.4 Homework

Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 4.4 Homework Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 4.4 Homework 4.65 You buy a hot stock for $1000. The stock either gains 30% or loses 25% each day, each with probability.

More information

A Simple Example. Sample Space and Event. Tree Diagram. Tree Diagram. Probability. Probability - 1. Probability and Counting Rules

A Simple Example. Sample Space and Event. Tree Diagram. Tree Diagram. Probability. Probability - 1. Probability and Counting Rules Probability and Counting Rules researcher claims that 10% of a large population have disease H. random sample of 100 people is taken from this population and examined. If 20 people in this random sample

More information

Review of Probability

Review of Probability Review of Probability Table of Contents Part I: Basic Equations and Notions Sample space Event Mutually exclusive Probability Conditional probability Independence Addition rule Multiplicative rule Using

More information

Determine the empirical probability that a person selected at random from the 1000 surveyed uses Mastercard.

Determine 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 information

Chapter 5 - Practice Problems 1

Chapter 5 - Practice Problems 1 Chapter 5 - Practice Problems 1 Identify the given random variable as being discrete or continuous. 1) The number of oil spills occurring off the Alaskan coast 1) A) Continuous B) Discrete 2) The ph level

More information

Chapter 5. Section 5.1: Central Tendency. Mode: the number or numbers that occur most often. Median: the number at the midpoint of a ranked data.

Chapter 5. Section 5.1: Central Tendency. Mode: the number or numbers that occur most often. Median: the number at the midpoint of a ranked data. Chapter 5 Section 5.1: Central Tendency Mode: the number or numbers that occur most often. Median: the number at the midpoint of a ranked data. Example 1: The test scores for a test were: 78, 81, 82, 76,

More information

Construct and Interpret Binomial Distributions

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

More information

Lesson 1: Experimental and Theoretical Probability

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.

More information

Elementary Statistics and Inference. Elementary Statistics and Inference. 16 The Law of Averages (cont.) 22S:025 or 7P:025.

Elementary 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 information

Example: If we roll a dice and flip a coin, how many outcomes are possible?

Example: If we roll a dice and flip a coin, how many outcomes are possible? 12.5 Tree Diagrams Sample space- Sample point- Counting principle- Example: If we roll a dice and flip a coin, how many outcomes are possible? TREE DIAGRAM EXAMPLE: Use a tree diagram to show all the possible

More information

Contemporary Mathematics- MAT 130. Probability. a) What is the probability of obtaining a number less than 4?

Contemporary 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 information

An Introduction to Basic Statistics and Probability

An Introduction to Basic Statistics and Probability An Introduction to Basic Statistics and Probability Shenek Heyward NCSU An Introduction to Basic Statistics and Probability p. 1/4 Outline Basic probability concepts Conditional probability Discrete Random

More information

AP Stats - Probability Review

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

More information

6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0.

6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0. Name: Date:. For each of the following scenarios, determine the appropriate distribution for the random variable X. A) A fair die is rolled seven times. Let X = the number of times we see an even number.

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Math 1342 (Elementary Statistics) Test 2 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the indicated probability. 1) If you flip a coin

More information

MATHEMATICS FOR ENGINEERS STATISTICS TUTORIAL 4 PROBABILITY DISTRIBUTIONS

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

More information

A (random) experiment is an activity with observable results. The sample space S of an experiment is the set of all outcomes.

A (random) experiment is an activity with observable results. The sample space S of an experiment is the set of all outcomes. Chapter 7 Probability 7.1 Experiments, Sample Spaces, and Events A (random) experiment is an activity with observable results. The sample space S of an experiment is the set of all outcomes. Each outcome

More information

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 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

More information

AP Statistics 7!3! 6!

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!

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Ch. - Problems to look at Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability

More information

MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW. Ch 1-3. One problem similar to the problems below will be included in the final

MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW. Ch 1-3. One problem similar to the problems below will be included in the final MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW Ch 1-3 One problem similar to the problems below will be included in the final 1.This table presents the price distribution of shoe styles offered

More information

An event is any set of outcomes of a random experiment; that is, any subset of the sample space of the experiment. The probability of a given event

An event is any set of outcomes of a random experiment; that is, any subset of the sample space of the experiment. The probability of a given event An event is any set of outcomes of a random experiment; that is, any subset of the sample space of the experiment. The probability of a given event is the sum of the probabilities of the outcomes in the

More information

You flip a fair coin four times, what is the probability that you obtain three heads.

You flip a fair coin four times, what is the probability that you obtain three heads. Handout 4: Binomial Distribution Reading Assignment: Chapter 5 In the previous handout, we looked at continuous random variables and calculating probabilities and percentiles for those type of variables.

More information

MAT 1000. Mathematics in Today's World

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

More information

Chapter 4: Probabilities and Proportions

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,

More information

STAT 319 Probability and Statistics For Engineers PROBABILITY. Engineering College, Hail University, Saudi Arabia

STAT 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 information

Distributions. and Probability. Find the sample space of an experiment. Find the probability of an event. Sample Space of an Experiment

Distributions. and Probability. Find the sample space of an experiment. Find the probability of an event. Sample Space of an Experiment C Probability and Probability Distributions APPENDIX C.1 Probability A1 C.1 Probability Find the sample space of an experiment. Find the probability of an event. Sample Space of an Experiment When assigning

More information

INTRODUCTION TO PROBABILITY AND STATISTICS

INTRODUCTION TO PROBABILITY AND STATISTICS INTRODUCTION TO PROBABILITY AND STATISTICS Conditional probability and independent events.. A fair die is tossed twice. Find the probability of getting a 4, 5, or 6 on the first toss and a,,, or 4 on the

More information

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

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

More information

Section 6-5 Sample Spaces and Probability

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)

More information

Chapter 6 ATE: Random Variables Alternate Examples and Activities

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.

More information

Math 1070 Exam 2B 22 March, 2013

Math 1070 Exam 2B 22 March, 2013 Math 1070 Exam 2B 22 March, 2013 This exam will last 50 minutes and consists of 13 multiple choice and 6 free response problems. Write your answers in the space provided. All solutions must be sufficiently

More information

Computing Binomial Probabilities

Computing Binomial Probabilities The Binomial Model The binomial probability distribution is a discrete probability distribution function Useful in many situations where you have numerical variables that are counts or whole numbers Classic

More information

MT426 Notebook 3 Fall 2012 prepared by Professor Jenny Baglivo. 3 MT426 Notebook 3 3. 3.1 Definitions... 3. 3.2 Joint Discrete Distributions...

MT426 Notebook 3 Fall 2012 prepared by Professor Jenny Baglivo. 3 MT426 Notebook 3 3. 3.1 Definitions... 3. 3.2 Joint Discrete Distributions... MT426 Notebook 3 Fall 2012 prepared by Professor Jenny Baglivo c Copyright 2004-2012 by Jenny A. Baglivo. All Rights Reserved. Contents 3 MT426 Notebook 3 3 3.1 Definitions............................................

More information

Thursday, November 13: 6.1 Discrete Random Variables

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.

More information

**Chance behavior is in the short run but has a regular and predictable pattern in the long run. This is the basis for the idea of probability.

**Chance behavior is in the short run but has a regular and predictable pattern in the long run. This is the basis for the idea of probability. AP Statistics Chapter 5 Notes 5.1 Randomness, Probability,and Simulation In tennis, a coin toss is used to decide which player will serve first. Many other sports use this method because it seems like

More information

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

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

More information

Topic 5 Review [81 marks]

Topic 5 Review [81 marks] Topic 5 Review [81 marks] A four-sided die has three blue faces and one red face. The die is rolled. Let B be the event a blue face lands down, and R be the event a red face lands down. 1a. Write down

More information

EXAM. Exam #3. Math 1430, Spring 2002. April 21, 2001 ANSWERS

EXAM. 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 information

Review for Test 2. Chapters 4, 5 and 6

Review for Test 2. Chapters 4, 5 and 6 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

More information

Chapter 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? 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 information

Chapter 4 Lecture Notes

Chapter 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 information

Chapter 4: Probability and Counting Rules

Chapter 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 information

ST 371 (IV): Discrete Random Variables

ST 371 (IV): Discrete Random Variables ST 371 (IV): Discrete Random Variables 1 Random Variables A random variable (rv) is a function that is defined on the sample space of the experiment and that assigns a numerical variable to each possible

More information

Section 6.2 Definition of Probability

Section 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 information

14.4. Expected Value Objectives. Expected Value

14.4. Expected Value Objectives. Expected Value . Expected Value Objectives. Understand the meaning of expected value. 2. Calculate the expected value of lotteries and games of chance.. Use expected value to solve applied problems. Life and Health Insurers

More information

AQA Statistics 1. Probability. Section 2: Tree diagrams

AQA Statistics 1. Probability. Section 2: Tree diagrams Notes and Examples AQA Statistics Probability Section 2: Tree diagrams These notes include sub-sections on; Reminder of the addition and multiplication rules Probability tree diagrams Problems involving

More information

Chapter 6 Continuous Probability Distributions

Chapter 6 Continuous Probability Distributions Continuous Probability Distributions Learning Objectives 1. Understand the difference between how probabilities are computed for discrete and continuous random variables. 2. Know how to compute probability

More information

Probability. Sample space: all the possible outcomes of a probability experiment, i.e., the population of outcomes

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

More information

STT 315 Practice Problems II for Sections

STT 315 Practice Problems II for Sections STT 315 Practice Problems II for Sections 4.1-4.8 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Classify the following random

More information

Introductory Probability. MATH 107: Finite Mathematics University of Louisville. March 5, 2014

Introductory 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 information

Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions.

Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions. Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

More information

AP Stats Fall Final Review Ch. 5, 6

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

More information

Probability OPRE 6301

Probability OPRE 6301 Probability OPRE 6301 Random Experiment... Recall that our eventual goal in this course is to go from the random sample to the population. The theory that allows for this transition is the theory of probability.

More information

The Normal Approximation to Probability Histograms. Dice: Throw a single die twice. The Probability Histogram: Area = Probability. Where are we going?

The Normal Approximation to Probability Histograms. Dice: Throw a single die twice. The Probability Histogram: Area = Probability. Where are we going? The Normal Approximation to Probability Histograms Where are we going? Probability histograms The normal approximation to binomial histograms The normal approximation to probability histograms of sums

More information

THE MULTINOMIAL DISTRIBUTION. Throwing Dice and the Multinomial Distribution

THE MULTINOMIAL DISTRIBUTION. Throwing Dice and the Multinomial Distribution THE MULTINOMIAL DISTRIBUTION Discrete distribution -- The Outcomes Are Discrete. A generalization of the binomial distribution from only 2 outcomes to k outcomes. Typical Multinomial Outcomes: red A area1

More information

Discrete Random Variables and their Probability Distributions

Discrete Random Variables and their Probability Distributions CHAPTER 5 Discrete Random Variables and their Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Discrete Random Variable

More information

For 2 coins, it is 2 possible outcomes for the first coin AND 2 possible outcomes for the second coin

For 2 coins, it is 2 possible outcomes for the first coin AND 2 possible outcomes for the second coin Problem Set 1. 1. If you have 10 coins, how many possible combinations of heads and tails are there for all 10 coins? Hint: how many combinations for one coin; two coins; three coins? Here there are 2

More information

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

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. Find the mean for the given sample data. 1) Bill kept track of the number of hours he spent

More information

C.4 Tree Diagrams and Bayes Theorem

C.4 Tree Diagrams and Bayes Theorem A26 APPENDIX C Probability and Probability Distributions C.4 Tree Diagrams and Bayes Theorem Find probabilities using tree diagrams. Find probabilities using Bayes Theorem. Tree Diagrams A type of diagram

More information

Find an expected value involving two events. Find an expected value involving multiple events. Use expected value to make investment decisions.

Find 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 information

36 Odds, Expected Value, and Conditional Probability

36 Odds, Expected Value, and Conditional Probability 36 Odds, Expected Value, and Conditional Probability What s the difference between probabilities and odds? To answer this question, let s consider a game that involves rolling a die. If one gets the face

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Exam Name 1) Solve the system of linear equations: 2x + 2y = 1 3x - y = 6 2) Consider the following system of linear inequalities. 5x + y 0 5x + 9y 180 x + y 5 x 0, y 0 1) 2) (a) Graph the feasible set

More information

2. Three dice are tossed. Find the probability of a) a sum of 4; or b) a sum greater than 4 (may use complement)

2. 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 information

Probability Review. ICPSR Applied Bayesian Modeling

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

More information

Generating Random Data. Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.edu

Generating Random Data. Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.edu Generating Random Data Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.edu Spring 2006 R Notes 1 Copyright c 2006 Alan T. Arnholt 2 Generating Random

More information

MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.

MA 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 information

If a tennis player was selected at random from the group, find the probability that the player is

If a tennis player was selected at random from the group, find the probability that the player is Basic Probability. The table below shows the number of left and right handed tennis players in a sample of 0 males and females. Left handed Right handed Total Male 3 29 32 Female 2 6 8 Total 4 0 If a tennis

More information

6.1. Construct and Interpret Binomial Distributions. p Study probability distributions. Goal VOCABULARY. Your Notes.

6.1. Construct and Interpret Binomial Distributions. p Study probability distributions. Goal VOCABULARY. Your Notes. 6.1 Georgia Performance Standard(s) MM3D1 Your Notes Construct and Interpret Binomial Distributions Goal p Study probability distributions. VOCABULARY Random variable Discrete random variable Continuous

More information

Practice Questions Chapter 4 & 5

Practice Questions Chapter 4 & 5 Practice Questions Chapter 4 & 5 Use the following to answer questions 1-3: Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a

More information

Jan 17 Homework Solutions Math 151, Winter 2012. Chapter 2 Problems (pages 50-54)

Jan 17 Homework Solutions Math 151, Winter 2012. Chapter 2 Problems (pages 50-54) Jan 17 Homework Solutions Math 11, Winter 01 Chapter Problems (pages 0- Problem In an experiment, a die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample

More information

Statistics 100A Homework 2 Solutions

Statistics 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 information

PROBLEM SET 1. For the first three answer true or false and explain your answer. A picture is often helpful.

PROBLEM SET 1. For the first three answer true or false and explain your answer. A picture is often helpful. PROBLEM SET 1 For the first three answer true or false and explain your answer. A picture is often helpful. 1. Suppose the significance level of a hypothesis test is α=0.05. If the p-value of the test

More information

STAB47S:2003 Midterm Name: Student Number: Tutorial Time: Tutor:

STAB47S:2003 Midterm Name: Student Number: Tutorial Time: Tutor: STAB47S:200 Midterm Name: Student Number: Tutorial Time: Tutor: Time: 2hours Aids: The exam is open book Students may use any notes, books and calculators in writing this exam Instructions: Show your reasoning

More information

x = the number of trials until the first success is observed p = probability of "success" on a single trial Mean (Expected value)

x = the number of trials until the first success is observed p = probability of success on a single trial Mean (Expected value) BINOMIAL PROBABILITY DISTRIBUTION n k nk px ( k) p 1 p k Mean (Expected value) = np Variance 2 = np(1 p) Standard Deviation σ np(1 p) RANDOM VARIABLES Mean = xi p xi 2 Standard Deviation = x px i 1. Among

More information

6.3 Conditional Probability and Independence

6.3 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 information

CHAPTER 4: DISCRETE RANDOM VARIABLE

CHAPTER 4: DISCRETE RANDOM VARIABLE CHAPTER 4: DISCRETE RANDOM VARIABLE Exercise 1. A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following

More information