, the of all of a probability experiment. consists of outcomes. (b) List the elements of the event consisting of a number that is greater than 4.


 Shanon Hawkins
 4 years ago
 Views:
Transcription
1 41 Sample Spaces and Probability as a general concept can be defined as the chance of an event occurring. In addition to being used in games of chance, probability is used in the fields of,, and forecasting, and in various areas. 42 Defns any activity that leads to welldefined results called,the result of a single trial of a probability., the of all of a probability experiment. a of the sample space. an event with outcome. consists of outcomes. (a) A die is tossed one time. List the elements of the sample space S. (b) List the elements of the event consisting of a number that is greater than 4. Example 2 A coin is tossed twice. List the elements of the sample space S, and list the elements of the event consisting of at least one head. [Using a tree diagram:] Example 3 A randomly selected citizen is interviewed and the following information is recorded: employment status and level of education. The symbols for employment status are Y = employed and N = unemployed, and the symbols for level of education are 1 = did not complete high school, 2 = completed high school but did not complete college, and 3 = completed college.
2 II. Calculating Probabilities 1. ( Approximation of Probability) An experiment is performed, and then the number of times that event A actually. Based on these actual results, P(A) is estimated by the of A. P(A) Rounding Rule Probabilities should be expressed as fractions or rounded to or decimal places. When the probability of an event is an extremely decimal, it is permissible to round the decimal to the first digit after the decimal point. Example 1 : The age distribution of employees for this college is shown below: Age # of employees Under 20 If an employee is selected at, find the probability that he or she is in the following age groups. (a) Between 30 and 39 years of age (b) Under 20 or over 49 years or age Example 2During a sale at men s store, 16 white sweaters, 3 red sweaters, 9 blue sweaters, and 7 yellow sweaters were purchased. If a customer is selected at random, find the probability that he bought a sweater that was. 2. Approach to Probability (Requires Outcomes) Suppose that A is an event in a sample space S and each outcome in S is. Let n(a) represent the number of outcomes in A and n(s) represent the total number of outcomes in S. Then P(A)=
3 Example 1 A statistics class contains 14 males and 20 females. A student is to be selected by chance and the gender of the student recorded. (a) Use the Classical Approach to Probability to find P(M) and P(F). S= P(M)= P(F)= (b) Is each outcome equally likely? Explain. (C) Use the Empirical Approach to find P(M) and P(F) based on the data obtained. Example: Two dice are tossed. Find the probability that the sum of two dice is greater than 8? S= Example 3 : If one card is drawn from a deck, find the probability of getting (a) a club (b) a 4 and a club
4 Example 4 Three equally qualified runners, Mark (M), Bill (B) and Alan (A), run a 100meter, sprint, and the order of finish is recorded. (a) Give a sample space S. (b) What is the probability that Mark will finish last? uses a probability value based on an educated or, employing opinions and information. In probability, a person or group makes an educated guess at the that an event will occur. This guess is based on the person s experience and evaluation of a solution. III. Requirements for Probabilities 1.) 2.) Probabilities should be expressed as fractions or rounded to or decimal places. Example 1: A probability experiment is conducted. Which of these can be considered a probability of an outcome and why? (a) 2 / 5 (b) (c) 1.09 Example 2: Given: S = {E1, E2, E3, E4}, and P(E1) = P(E2) = 0.2 and P(E3) = 0.5, find P(E4)
5 IV. The Complement Rule The of event A is the set of in the sample space that are included in the outcomes of event A. For any event A, the probability of its complement is Example 1 The chance of raining tomorrow is 70%. What is probability that it will not rain tomorrow? 42 The Addition Rules for Probability I. Addition Rule for Mutually Exclusive Events Event A and B are if they occur together when the experiment is performed. (e.g. no elements) If A, B are mutually exclusive events, then P (A or B) = Example 1 A single card is drawn from a deck. Find the probability of selecting a club or a diamond. Example 2 In a large department store, there are 2 managers, 4 department heads, 16 clerks, and 4 stock persons. If a person is selected at random, find the probability that the person is either a clerk or a manager. II. General Addition Rule If A, and B are mutually exclusive events, then P (A or B) = Example 1 A single card is drawn from a deck. Find the probability of selecting a jack or a black card.
6 Example 2 In a certain geographic region, newspapers are classified as being published daily morning, daily evening, and weekly. Some have a comics section and other do not. The distribution is shown here. Yes No Having comics Section Morning Evening Weekly If a newspaper is selected at random, find these probabilities. (a) The newspaper is weekly publication. (b) The newspaper is a daily morning publication or has comics. (c) The newspaper is published weekly or does not have comics.
7 Section 4 3 I. Multiplication Rule for Independent Events Events A and B are if the outcome of event A has on the outcome of event B. Suppose A and B are independent events, then P (A and B) = Example 1: If 36% of college students are overweight, find the probability that if three college students are selected at random, all will be overweight. Example 2: If 25% of U.S. federal prison inmates are not U.S. citizens, find the probability that two randomly selected federal prison inmates will be U.S. citizens. Example 3:Suppose the probability of remaining with a particular company 10 years or longer is 1/6. A man and a woman start work at the company on the same day. (a) What is the probability that the man will work there less than 10 years? (b) What is the probability that both the man and woman will work there less than 10 years? Example 4: A smokedetector system uses two devices, A and B. If smoke is present, the probability that it will be detected by device A is 0.95; by device B, 0.98; and by both devices, (a) If smoke is present, find the probability that the smoke will be detected by device A or device B or by both devices. (b) Find the probability that the smoke will not be detected.
8 Example 5:If you make random guesses for four multiplechoice test questions (each with five possible answers), what is the probability of getting at least one correct? Example 6: There are 2000 voters in a town. Consider the experiment of randomly selecting a voter to be interviewed. The event A consists of being in favor of more stringent building codes; the event B consists of having lived in the town less than 10 years. The following table gives the number of voters in various categories. a.) b.) c.) II. Multiplication Rule for Dependent Events Events A and B are if the outcome of event A the outcome of event B. Suppose A and B are dependent events, then P (A and B) = Example 1:A box has 5 red balls and 2 white balls. If two balls are randomly selected (one after the other), what is the probability that they both are red? (a) With replacement (independent case) b) Without replacement (dependent case)
9 Ex 2: Three cards are drawn from a deck without replacement. Find the probability that all are Jacks. III. Conditional Probability The probability that B occurs that A has can be found by the probability that events occurred by the probability that the first event (A) has occurred. P(B A) = Example 1: Two fair dice are tossed. Consider the following events. A = sum is 7 or more, B = sum is even, C = a match (both numbers are the same). S = the sample space is the same as we did previously Find the events in the sets A, B, and C. What is P(A), P(B), P(C)? a.) What is P(A and B)? b.) What is P (A or B) (c) P (A B) = (d) P (B C) =
10 Example 2 :At a local Country Club, 65% of the members play bridge and swim, and 72% play bridge. If a member is selected at random, find the probability that the member swims, given that the member plays bridge. Example 3 : Eighty students in a school cafeteria were asked if they favored a ban on smoking in the cafeteria. The results of the survey are shown in the table. Class Favor Oppose No opinion Freshman Sophomore If a student is selected at random, find these probabilities. (a) The student is a freshman or favors the ban. (b) Given that the student favors the ban, the student is a sophomore. Section 44 I. Principle of Counting If Task 1 can be done in n ways and Task 2 in m ways, Task 1 and Task 2 performed together can be done in. (Also called the Multiplication Rule) Example 1 : Two dice are tossed. How many outcomes are in S. Example 2 :A password consists of two letters followed by one digit. How many different passwords can be created? (Note: Repetitions are allowed) Example 3 : Suppose four digits are to be randomly selected (with repetitions allowed). (Note: the set of digits is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.) If the first digit must be a 2 and repetitions are permitted, how many different 4digit can be made?
11 Permutations The number of ways we can n objects, them r at a time, is : npr = Combinations The number of combinations of n objects can be formed, them r at a time is ncr= Note: Combinations are always than permutations for the same n and r. Example 1 : a.) b.) c.) d.) Example 2: An inspector must select 3 tests to performed in a certain order on a manufactured part. He has a choice of 7 tests. How many ways can be performed 3 different tests? Example 3: If a person can select 3 presents from 10 presents, how many different combinations are there? Example 4: Your family vacation involves a crosscountry air flight, a rental car, and a hotel stay in Boston. If you can choose from four major air carriers, five car rental agencies, and three major hotel chains, how many options are available for your vacation accommodations?
12 Section 4 5 I. Probability and Counting Rules Use the multiplication rule, combination and permutation learned from Section 45 to the number of ways to a given event, n(a), and to the number of ways for the of an experiment, n(s). The probability of A = P(A) = Ex 1: A combination lock consists of 26 letters of the alphabet. If a threeletter combination is needed, find the probability that the combination will consist of the first two letters AB in that order. The same letter can be used more than once. Ex 2: Five cards are selected from a 52card deck for a poker hand. (a) How many outcomes are in the sample space? b.) A royal flush is a hand that contains that A, K, Q, J, 10, all in the same suit. How many ways are there to get a royal flush? c) What is the probability of being dealt a royal flush?
Math 227 Elementary Statistics. Bluman 5 th edition
Math 227 Elementary Statistics Bluman 5 th edition CHAPTER 4 Probability and Counting Rules 2 Objectives Determine sample spaces and find the probability of an event using classical probability or empirical
More information1. How to identify the sample space of a probability experiment and how to identify simple events
Statistics Chapter 3 Name: 3.1 Basic Concepts of Probability Learning objectives: 1. How to identify the sample space of a probability experiment and how to identify simple events 2. How to use the Fundamental
More informationSection 6.5 Conditional Probability
Section 6.5 Conditional Probability Example 1: An urn contains 5 green marbles and 7 black marbles. Two marbles are drawn in succession and without replacement from the urn. a) What is the probability
More informationMath 1313 Section 6.2 Definition of Probability
Math 1313 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
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Statistics Homework Ch 5 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability
More informationSection Introduction to Sets
Section 1.1  Introduction to Sets Definition: A set is a welldefined collection of objects usually denoted by uppercase letters. Definition: The elements, or members, of a set are denoted by lowercase
More informationChapter 4. Probability and Counting Rules. McGrawHill, Bluman, 7 th ed, Chapter 4
Chapter 4 Probability and Counting Rules McGrawHill, Bluman, 7 th ed, Chapter 4 Chapter 4 Overview Introduction 41 Sample Spaces and Probability 42 Addition Rules for Probability 43 Multiplication
More informationChapter 3: PROBABILITY
Chapter 3 Math 3201 1 3.1 Exploring Probability: P(event) = Chapter 3: PROBABILITY number of outcomes favourable to the event total number of outcomes in the sample space An event is any collection of
More informationProbability Concepts and Counting Rules
Probability Concepts and Counting Rules Chapter 4 McGrawHill/Irwin Dr. Ateq Ahmed AlGhamedi Department of Statistics P O Box 80203 King Abdulaziz University Jeddah 21589, Saudi Arabia ateq@kau.edu.sa
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 information4.1 Sample Spaces and Events
4.1 Sample Spaces and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment is called an
More informationEmpirical (or statistical) probability) is based on. The empirical probability of an event E is the frequency of event E.
Probability and Statistics Chapter 3 Notes Section 31 I. Probability Experiments. A. When weather forecasters say There is a 90% chance of rain tomorrow, or a doctor says There is a 35% chance of a successful
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Study Guide for Test III (MATH 1630) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the number of subsets of the set. 1) {x x is an even
More informationCHAPTER 9  COUNTING PRINCIPLES AND PROBABILITY
CHAPTER 9  COUNTING PRINCIPLES AND PROBABILITY Probability is the Probability is used in many realworld fields, such as insurance, medical research, law enforcement, and political science. Objectives:
More informationProbability  Chapter 4
Probability  Chapter 4 In this chapter, you will learn about probability its meaning, how it is computed, and how to evaluate it in terms of the likelihood of an event actually happening. A cynical person
More information7.1 Experiments, Sample Spaces, and Events
7.1 Experiments, Sample Spaces, and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment
More information4.3 Rules of Probability
4.3 Rules of Probability If a probability distribution is not uniform, to find the probability of a given event, add up the probabilities of all the individual outcomes that make up the event. Example:
More informationChapter 3: Elements of Chance: Probability Methods
Chapter 3: Elements of Chance: Methods Department of Mathematics Izmir University of Economics Week 34 20142015 Introduction In this chapter we will focus on the definitions of random experiment, outcome,
More information05 Adding Probabilities. 1. CARNIVAL GAMES A spinner has sections of equal size. The table shows the results of several spins.
1. CARNIVAL GAMES A spinner has sections of equal size. The table shows the results of several spins. d. a. Copy the table and add a column to show the experimental probability of the spinner landing on
More informationBusiness Statistics. Chapter 4 Using Probability and Probability Distributions QMIS 120. Dr. Mohammad Zainal
Department of Quantitative Methods & Information Systems Business Statistics Chapter 4 Using Probability and Probability Distributions QMIS 120 Dr. Mohammad Zainal Chapter Goals After completing this chapter,
More informationProbability. The MEnTe Program Math Enrichment through Technology. Title V East Los Angeles College
Probability The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College 2003 East Los Angeles College. All rights reserved. Topics Introduction Empirical Probability Theoretical
More informationChapter 1. Probability
Chapter 1. Probability 1.1 Basic Concepts Scientific method a. For a given problem, we define measures that explains the problem well. b. Data is collected with observation and the measures are calculated.
More informationPROBABILITY. 1. Introduction. Candidates should able to:
PROBABILITY Candidates should able to: evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events (e.g for the total score when two fair dice are thrown), or by calculation
More informationNovember 6, Chapter 8: Probability: The Mathematics of Chance
Chapter 8: Probability: The Mathematics of Chance November 6, 2013 Last Time Crystallographic notation Groups Crystallographic notation The first symbol is always a p, which indicates that the pattern
More informationProbability Review 41
Probability Review 41 For the following problems, give the probability to four decimals, or give a fraction, or if necessary, use scientific notation. Use P(A) = 1  P(not A) 1) A coin is tossed 6 times.
More informationECON 214 Elements of Statistics for Economists
ECON 214 Elements of Statistics for Economists Session 4 Probability Lecturer: Dr. Bernardin Senadza, Dept. of Economics Contact Information: bsenadza@ug.edu.gh College of Education School of Continuing
More informationChapter 1: Sets and Probability
Chapter 1: Sets and Probability Section 1.31.5 Recap: Sample Spaces and Events An is an activity that has observable results. An is the result of an experiment. Example 1 Examples of experiments: Flipping
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Chapter 3: Practice SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. ) A study of 000 randomly selected flights of a major
More informationSection 6.1 #16. Question: What is the probability that a fivecard poker hand contains a flush, that is, five cards of the same suit?
Section 6.1 #16 What is the probability that a fivecard poker hand contains a flush, that is, five cards of the same suit? page 1 Section 6.1 #38 Two events E 1 and E 2 are called independent if p(e 1
More informationProbability. March 06, J. Boulton MDM 4U1. P(A) = n(a) n(s) Introductory Probability
Most people think they understand odds and probability. Do you? Decision 1: Pick a card Decision 2: Switch or don't Outcomes: Make a tree diagram Do you think you understand probability? Probability Write
More informationAnswer each of the following problems. Make sure to show your work.
Answer each of the following problems. Make sure to show your work. 1. A board game requires each player to roll a die. The player with the highest number wins. If a player wants to calculate his or her
More informationChapter 5  Elementary Probability Theory
Chapter 5  Elementary Probability Theory Historical Background Much of the early work in probability concerned games and gambling. One of the first to apply probability to matters other than gambling
More informationRaise your hand if you rode a bus within the past month. Record the number of raised hands.
166 CHAPTER 3 PROBABILITY TOPICS Raise your hand if you rode a bus within the past month. Record the number of raised hands. Raise your hand if you answered "yes" to BOTH of the first two questions. Record
More informationChapter 1. Probability
Chapter 1. Probability 1.1 Basic Concepts Scientific method a. For a given problem, we define measures that explains the problem well. b. Data is collected with observation and the measures are calculated.
More informationProbability and Statistics 15% of EOC
MGSE912.S.CP.1 1. Which of the following is true for A U B A: 2, 4, 6, 8 B: 5, 6, 7, 8, 9, 10 A. 6, 8 B. 2, 4, 6, 8 C. 2, 4, 5, 6, 6, 7, 8, 8, 9, 10 D. 2, 4, 5, 6, 7, 8, 9, 10 2. This Venn diagram shows
More informationProbability Rules. 2) The probability, P, of any event ranges from which of the following?
Name: WORKSHEET : Date: Answer the following questions. 1) Probability of event E occurring is... P(E) = Number of ways to get E/Total number of outcomes possible in S, the sample space....if. 2) The probability,
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Mathematical Ideas Chapter 2 Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) In one town, 2% of all voters are Democrats. If two voters
More informationAP Statistics Ch InClass Practice (Probability)
AP Statistics Ch 1415 InClass Practice (Probability) #1a) A batter who had failed to get a hit in seven consecutive times at bat then hits a gamewinning home run. When talking to reporters afterward,
More information2. The figure shows the face of a spinner. The numbers are all equally likely to occur.
MYP IB Review 9 Probability Name: Date: 1. For a carnival game, a jar contains 20 blue marbles and 80 red marbles. 1. Children take turns randomly selecting a marble from the jar. If a blue marble is chosen,
More informationHere are other examples of independent events:
5 The Multiplication Rules and Conditional Probability The Multiplication Rules Objective. Find the probability of compound events using the multiplication rules. The previous section showed that the addition
More informationChapter 4: Probability and Counting Rules
Chapter 4: Probability and Counting Rules Before we can move from descriptive statistics to inferential statistics, we need to have some understanding of probability: Ch4: Probability and Counting Rules
More informationProbability and Counting Techniques
Probability and Counting Techniques Diana Pell (Multiplication Principle) Suppose that a task consists of t choices performed consecutively. Suppose that choice 1 can be performed in m 1 ways; for each
More informationMathematics 'A' level Module MS1: Statistics 1. Probability. The aims of this lesson are to enable you to. calculate and understand probability
Mathematics 'A' level Module MS1: Statistics 1 Lesson Three Aims The aims of this lesson are to enable you to calculate and understand probability apply the laws of probability in a variety of situations
More informationMath 141 Exam 3 Review with Key. 1. P(E)=0.5, P(F)=0.6 P(E F)=0.9 Find ) b) P( E F ) c) P( E F )
Math 141 Exam 3 Review with Key 1. P(E)=0.5, P(F)=0.6 P(E F)=0.9 Find C C C a) P( E F) ) b) P( E F ) c) P( E F ) 2. A fair coin is tossed times and the sequence of heads and tails is recorded. Find a)
More information1) If P(E) is the probability that an event will occur, then which of the following is true? (1) 0 P(E) 1 (3) 0 P(E) 1 (2) 0 P(E) 1 (4) 0 P(E) 1
Algebra 2 Review for Unit 14 Test Name: 1) If P(E) is the probability that an event will occur, then which of the following is true? (1) 0 P(E) 1 (3) 0 P(E) 1 (2) 0 P(E) 1 (4) 0 P(E) 1 2) From a standard
More information3 The multiplication rule/miscellaneous counting problems
Practice for Exam 1 1 Axioms of probability, disjoint and independent events 1. Suppose P (A) = 0.4, P (B) = 0.5. (a) If A and B are independent, what is P (A B)? What is P (A B)? (b) If A and B are disjoint,
More informationSuch a description is the basis for a probability model. Here is the basic vocabulary we use.
5.2.1 Probability Models When we toss a coin, we can t know the outcome in advance. What do we know? We are willing to say that the outcome will be either heads or tails. We believe that each of these
More informationProbability as a general concept can be defined as the chance of an event occurring.
3. Probability In this chapter, you will learn about probability its meaning, how it is computed, and how to evaluate it in terms of the likelihood of an event actually happening. Probability as a general
More informationMath 3201 Unit 3: Probability Name:
Multiple Choice Math 3201 Unit 3: Probability Name: 1. Given the following probabilities, which event is most likely to occur? A. P(A) = 0.2 B. P(B) = C. P(C) = 0.3 D. P(D) = 2. Three events, A, B, and
More information[Independent Probability, Conditional Probability, Tree Diagrams]
Name: Year 1 Review 119 Topic: Probability Day 2 Use your formula booklet! Page 5 Lesson 118: Probability Day 1 [Independent Probability, Conditional Probability, Tree Diagrams] Read and Highlight Station
More informationContents 2.1 Basic Concepts of Probability Methods of Assigning Probabilities Principle of Counting  Permutation and Combination 39
CHAPTER 2 PROBABILITY Contents 2.1 Basic Concepts of Probability 38 2.2 Probability of an Event 39 2.3 Methods of Assigning Probabilities 39 2.4 Principle of Counting  Permutation and Combination 39 2.5
More informationNorth Seattle Community College Winter ELEMENTARY STATISTICS 2617 MATH Section 05, Practice Questions for Test 2 Chapter 3 and 4
North Seattle Community College Winter 2012 ELEMENTARY STATISTICS 2617 MATH 109  Section 05, Practice Questions for Test 2 Chapter 3 and 4 1. Classify each statement as an example of empirical probability,
More informationSection 7.1 Experiments, Sample Spaces, and Events
Section 7.1 Experiments, Sample Spaces, and Events Experiments An experiment is an activity with observable results. 1. Which of the follow are experiments? (a) Going into a room and turning on a light.
More informationChapter 6: Probability and Simulation. The study of randomness
Chapter 6: Probability and Simulation The study of randomness Introduction Probability is the study of chance. 6.1 focuses on simulation since actual observations are often not feasible. When we produce
More informationMath Exam 2 Review. NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5.
Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166  Exam 2 Review NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5. Section 7.1  Experiments, Sample Spaces,
More informationMath Exam 2 Review. NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5.
Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166  Exam 2 Review NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5. Section 7.1  Experiments, Sample Spaces,
More informationMath 1342 Exam 2 Review
Math 1342 Exam 2 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) If a sportscaster makes an educated guess as to how well a team will do this
More informationLecture 6 Probability
Lecture 6 Probability Example: When you toss a coin, there are only two possible outcomes, heads and tails. What if we toss a coin two times? Figure below shows the results of tossing a coin 5000 times
More informationProbability Models. Section 6.2
Probability Models Section 6.2 The Language of Probability What is random? Empirical means that it is based on observation rather than theorizing. Probability describes what happens in MANY trials. Example
More informationProbability and Counting Rules. Chapter 3
Probability and Counting Rules Chapter 3 Probability as a general concept can be defined as the chance of an event occurring. Many people are familiar with probability from observing or playing games of
More informationReview Questions on Ch4 and Ch5
Review Questions on Ch4 and Ch5 1. Find the mean of the distribution shown. x 1 2 P(x) 0.40 0.60 A) 1.60 B) 0.87 C) 1.33 D) 1.09 2. A married couple has three children, find the probability they are all
More informationExam 2 Review F09 O Brien. Finite Mathematics Exam 2 Review
Finite Mathematics Exam Review Approximately 5 0% of the questions on Exam will come from Chapters, 4, and 5. The remaining 70 75% will come from Chapter 7. To help you prepare for the first part of the
More informationAlgebra 2 Notes Section 10.1: Apply the Counting Principle and Permutations
Algebra 2 Notes Section 10.1: Apply the Counting Principle and Permutations Objective(s): Vocabulary: I. Fundamental Counting Principle: Two Events: Three or more Events: II. Permutation: (top of p. 684)
More informationNormal Distribution Lecture Notes Continued
Normal Distribution Lecture Notes Continued 1. Two Outcome Situations Situation: Two outcomes (for against; heads tails; yes no) p = percent in favor q = percent opposed Written as decimals p + q = 1 Why?
More informationStat210 WorkSheet#2 Chapter#2
1. When rolling a die 5 times, the number of elements of the sample space equals.(ans.=7,776) 2. If an experiment consists of throwing a die and then drawing a letter at random from the English alphabet,
More informationBasic Probability Concepts
6.1 Basic Probability Concepts How likely is rain tomorrow? What are the chances that you will pass your driving test on the first attempt? What are the odds that the flight will be on time when you go
More informationExam III Review Problems
c Kathryn Bollinger and Benjamin Aurispa, November 10, 2011 1 Exam III Review Problems Fall 2011 Note: Not every topic is covered in this review. Please also take a look at the previous WeekinReviews
More informationS = {(1, 1), (1, 2),, (6, 6)}
Part, MULTIPLE CHOICE, 5 Points Each An experiment consists of rolling a pair of dice and observing the uppermost faces. The sample space for this experiment consists of 6 outcomes listed as pairs of numbers:
More informationMath 147 Elementary Probability/Statistics I Additional Exercises on Chapter 4: Probability
Math 147 Elementary Probability/Statistics I Additional Exercises on Chapter 4: Probability Student Name: Find the indicated probability. 1) If you flip a coin three times, the possible outcomes are HHH
More informationWeek 3 Classical Probability, Part I
Week 3 Classical Probability, Part I Week 3 Objectives Proper understanding of common statistical practices such as confidence intervals and hypothesis testing requires some familiarity with probability
More informationMath 146 Statistics for the Health Sciences Additional Exercises on Chapter 3
Math 46 Statistics for the Health Sciences Additional Exercises on Chapter 3 Student Name: Find the indicated probability. ) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH
More informationChapter 5 Probability
Chapter 5 Probability Math150 What s the likelihood of something occurring? Can we answer questions about probabilities using data or experiments? For instance: 1) If my parking meter expires, I will probably
More informationSection 11.4: Tree Diagrams, Tables, and Sample Spaces
Section 11.4: Tree Diagrams, Tables, and Sample Spaces Diana Pell Exercise 1. Use a tree diagram to find the sample space for the genders of three children in a family. Exercise 2. (You Try!) A soda machine
More informationChapter 11: Probability and Counting Techniques
Chapter 11: Probability and Counting Techniques Diana Pell Section 11.1: The Fundamental Counting Principle Exercise 1. How many different twoletter words (including nonsense words) can be formed when
More information, x {1, 2, k}, where k > 0. (a) Write down P(X = 2). (1) (b) Show that k = 3. (4) Find E(X). (2) (Total 7 marks)
1. The probability distribution of a discrete random variable X is given by 2 x P(X = x) = 14, x {1, 2, k}, where k > 0. Write down P(X = 2). (1) Show that k = 3. Find E(X). (Total 7 marks) 2. In a game
More informationNovember 8, Chapter 8: Probability: The Mathematics of Chance
Chapter 8: Probability: The Mathematics of Chance November 8, 2013 Last Time Probability Models and Rules Discrete Probability Models Equally Likely Outcomes Crystallographic notation The first symbol
More informationName: Class: Date: 6. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is 11
Class: Date: Sample Mastery # Multiple Choice Identify the choice that best completes the statement or answers the question.. One repetition of an experiment is known as a(n) random variable expected value
More information6) A) both; happy B) neither; not happy C) one; happy D) one; not happy
MATH 00  PRACTICE TEST 2 Millersville University, Spring 202 Ron Umble, Instr. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all natural
More informationA Probability Work Sheet
A Probability Work Sheet October 19, 2006 Introduction: Rolling a Die Suppose Geoff is given a fair sixsided die, which he rolls. What are the chances he rolls a six? In order to solve this problem, we
More informationChapter 11: Probability and Counting Techniques
Chapter 11: Probability and Counting Techniques Diana Pell Section 11.3: Basic Concepts of Probability Definition 1. A sample space is a set of all possible outcomes of an experiment. Exercise 1. An experiment
More informationThe point value of each problem is in the lefthand margin. You must show your work to receive any credit, except on problems 1 & 2. Work neatly.
Introduction to Statistics Math 1040 Sample Exam II Chapters 57 4 Problem Pages 4 Formula/Table Pages Time Limit: 90 Minutes 1 No Scratch Paper Calculator Allowed: Scientific Name: The point value of
More informationIf you roll a die, what is the probability you get a four OR a five? What is the General Education Statistics
If you roll a die, what is the probability you get a four OR a five? What is the General Education Statistics probability that you get neither? Class Notes The Addition Rule (for OR events) and Complements
More informationClass XII Chapter 13 Probability Maths. Exercise 13.1
Exercise 13.1 Question 1: Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E F) = 0.2, find P (E F) and P(F E). It is given that P(E) = 0.6, P(F) = 0.3, and P(E F) = 0.2 Question 2:
More informationChapter 6  Probability Review Questions
Chapter 6  Probability Review Questions Addition Rule: or union or & and (in the same problem) P( A B ) = P( A) + P( B) P( A B) *** If the events A and B are mutually exclusive (disjoint), then P ( A
More informationConditional Probability Worksheet
Conditional Probability Worksheet P( A and B) P(A B) = P( B) Exercises 36, compute the conditional probabilities P( AB) and P( B A ) 3. P A = 0.7, P B = 0.4, P A B = 0.25 4. P A = 0.45, P B = 0.8, P A
More informationProbability. The Bag Model
Probability The Bag Model Imagine a bag (or box) containing balls of various kinds having various colors for example. Assume that a certain fraction p of these balls are of type A. This means N = total
More informationProbability. Ms. Weinstein Probability & Statistics
Probability Ms. Weinstein Probability & Statistics Definitions Sample Space The sample space, S, of a random phenomenon is the set of all possible outcomes. Event An event is a set of outcomes of a random
More informationMath 1324 Finite Mathematics Sections 8.2 and 8.3 Conditional Probability, Independent Events, and Bayes Theorem
Finite Mathematics Sections 8.2 and 8.3 Conditional Probability, Independent Events, and Bayes Theorem What is conditional probability? It is where you know some information, but not enough to get a complete
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Ch. 3 Probability 3.1 Basic Concepts of Probability and Counting 1 Find Probabilities 1) A coin is tossed. Find the probability that the result is heads. A) 0. B) 0.1 C) 0.9 D) 1 2) A single sixsided
More informationBeginnings of Probability I
Beginnings of Probability I Despite the fact that humans have played games of chance forever (so to speak), it is only in the 17 th century that two mathematicians, Pierre Fermat and Blaise Pascal, set
More informationProbability Theory. Mohamed I. Riffi. Islamic University of Gaza
Probability Theory Mohamed I. Riffi Islamic University of Gaza Table of contents 1. Chapter 1 Probability Properties of probability Counting techniques 1 Chapter 1 Probability Probability Theorem P(φ)
More informationM146  Chapter 5 Handouts. Chapter 5
Chapter 5 Objectives of chapter: Understand probability values. Know how to determine probability values. Use rules of counting. Section 51 Probability Rules What is probability? It s the of the occurrence
More informationDef: The intersection of A and B is the set of all elements common to both set A and set B
Def: Sample Space the set of all possible outcomes Def: Element an item in the set Ex: The number "3" is an element of the "rolling a die" sample space Main concept write in Interactive Notebook Intersection:
More informationChapter 6: Probability and Simulation. The study of randomness
Chapter 6: Probability and Simulation The study of randomness 6.1 Randomness Probability describes the pattern of chance outcomes. Probability is the basis of inference Meaning, the pattern of chance outcomes
More informationMAT Midterm Review
MAT 120  Midterm Review Name Identify the population and the sample. 1) When 1094 American households were surveyed, it was found that 67% of them owned two cars. Identify whether the statement describes
More informationChapter 12: Probability & Statistics. Notes #2: Simple Probability and Independent & Dependent Events and Compound Events
Chapter 12: Probability & Statistics Notes #2: Simple Probability and Independent & Dependent Events and Compound Events Theoretical & Experimental Probability 1 2 Probability: How likely an event is to
More informationb) Find the exact probability of seeing both heads and tails in three tosses of a fair coin. (Theoretical Probability)
Math 1351 Activity 2(Chapter 11)(Due by EOC Mar. 26) Group # 1. A fair coin is tossed three times, and we would like to know the probability of getting both a heads and tails to occur. Here are the results
More informationInstructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include your name and student ID.
Math 3201 Unit 3 Probability Test 1 Unit Test Name: Part 1 Selected Response: Instructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include
More informationStatistics Intermediate Probability
Session 6 oscardavid.barrerarodriguez@sciencespo.fr April 3, 2018 and Sampling from a Population Outline 1 The Monty Hall Paradox Some Concepts: Event Algebra Axioms and Things About that are True Counting
More informationAnswer each of the following problems. Make sure to show your work.
Answer each of the following problems. Make sure to show your work. 1. A board game requires each player to roll a die. The player with the highest number wins. If a player wants to calculate his or her
More information