Exam III Review Math-132 (Sections 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 8.1, 8.2, 8.3)
|
|
- Noel May
- 5 years ago
- Views:
Transcription
1 1 Exam III Review Math-132 (Sections 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 8.1, 8.2, 8.3) On this exam, questions may come from any of the following topic areas: - Union and intersection of sets - Complement of sets - Constructing and interpreting Venn Diagrams - Applying the additive rule to counts in sets - Applying the additive rule to probabilities of events - Applying the additive rule to word problems - The multiplicative principle - Tree diagrams - Simple probability calculations - Mutually exclusive and independent random outcomes - Probabilities of mutually exclusive and independent outcomes - Calculating probability given the odds - Calculating the odds given probability - Calculating the expected value - Calculating the expected value for the information in a word problem - Conditional probability of dependent events - Conditional probability of independent events - Probability calculation using the Baye s theorem Sections 7.1 #1) If { } { } what is: a) b) #2) If { } { } { } Find [ { } ] #3) If { } { } { } and { } Find [ { } ] #4) If { } { } { } Find [ { } ]
2 2 #5) If { } { } { } Find [ { } ] #6) A class of 28 students were surveyed and asked if they ever had dogs or cats for pets at home. 8 students said they only had a dog; 6 students said they only had a cat; 10 students said they had a dog and a cat; and 4 students said they never had a dog or a cat. Create a Venn Diagram that captures this information. [ ] 6 Cats 10 Dogs 8 4 #7) Out of 65 students, 28 are taking English Composition and 35 are taking Chemistry. 11 students are taking both classes. a) Draw the Venn Diagram for this information. [ answer: Do you see how this is done? Hint: Draw the Venn Diagram and place the intersection number, first] English U Chemistry b) How many are in neither class? [answer: 13]
3 3 c) How many are taking at least one of the classes? [answer: 52] d) What is the probability that a student is taking English but not Chemistry? [answer: 0.262] e) What is the probability that a student is taking both classes? [answer: 0.169] f) What is the probability that a student is taking English, given that the student is taking chemistry? [answer: 0.314] #8) In a group of 58 students, 24 are taking algebra, 12 are taking biology, 19 are taking chemistry, 7 are taking algebra and biology, 11 are taking algebra and chemistry, 6 are taking biology and chemistry, and 4 are taking all three courses. a) Draw the Venn Diagram for this information. [answer: Shown below. Do you see how this is done? Hint: Place the intersection number for all three courses first and work your way outward.] 10 A B U 6 C 23 b) How many students are not taking any of these courses? [answer: 23 ] c) What is the probability that a student is not taking any of these courses? [answer: ] d) What is the probability that a student is taking algebra and biology but not chemistry? [answer: ] e) What is the probability that a student is taking only biology? [answer: ] f) What is the probability that a student is taking exactly two of these courses? [answer: ]
4 4 Section 7.2 #9) Find ( ), given that ( ) and ( ) and ( ) #10) Find ( ), given that ( ) and ( ) and ( ) #11) Find ( ), given that ( ) and ( ) and ( ) #12) Motors, Inc. manufactured 250 cars with a GPS system, 205 with satellite system, and 70 with both these options. How many cars were manufactured if every car has at least one of these options? #13) In a survey of 600 business travelers, it was found that of two daily newspapers, New York times, and Wall Street Journal, 360 read New York Times, 112 read New York Times and Wall Street Journal, and 56 read only Wall Street Journal. a) How many read New York Times or Wall Street Journal? b) How many did not read either New York Times or Wall Street Journal? Section 7.3 #14) A man has 13 shirts and 5 ties. How many different shirts and tie arrangements can he wear? #15) A restaurant offers 3 different salads, 6 different main courses, 13 different desserts, and 7 different drinks. How many different launches are possible? #16) How many different ways can 4 people be seated in a row of 4 seats? #17) How many 4-letter code words are possible using the first 5 letters of the alphabet with no letters repeated? [ ] How many codes are possible when letters are allowed to repeat?
5 5 Section 7.4 #18) Three letters are picked from the alphabet (repetitions are allowed, assume order is important). Find the number of outcomes in the sample space. #19) A ball is picked from a box containing 8 orange, 5 red, 4 blue, and 9 green balls. Find the probability that a green or an orange ball is picked. #20) The 2008 income of U.S. families is described in the table: Income Level Number of families (in thousands) <$25,000 28,943 $25,000 - $49,999 29,178 $50,000 - $74,999 20,975 $75,000 - $99,999 13,944 24,022 What is the probability that a randomly selected family has an income of less than $50,000? Section 7.5 #21) If events E and F belong to the same sample space, and ( ), ( ), ( )=0.40 find ( ) #22) If events E and F belong to the same sample space, and ( ), ( ), ( )=0.80 find ( ) #23) If events A and B are mutually exclusive and if ( ), ( ), find the probability ( ). #24) Determine the probability of E if the odds against E are 4 to 13. #25) Determine the probability of the event E if odds against E are 5 to 2. #26) Determine the probability of E if the odds in favor of E are 3 to 1.
6 6 #27) Determine the probability of E if the odds in favor of E are 1 to 1. #28) Determine the odds for and against the event E if ( ). [ ] #29) Determine the odds for and against the event F if ( ) [ ] #30) Determine the odds for and against the event F if ( ) [ ] #31) Suppose events A and B are independent, with ( ) and ( ). a) Find the odds for A. b) Find the odds for (i.e., the odds against A) #32) Events A and B are mutually exclusive, with ( ) and ( ). a) Find the odds for A b) Find the odds for (i.e., the odds against A) #33) Anne is taking courses in both mathematics and English. She estimates her probability of passing mathematics at 0.3 and English at 0.4, and she estimates her probability of passing at least one of them at What is her probability of passing both courses?
7 7 #34) In a survey of the number of TV sets in a house, the following probability table was constructed. Number of TV sets or more Probability Find the probability of a house having: a) 1 or 2 TV sets b) 1 or 2 or 3 TV sets c) At least 2 TV sets d) At most 3 TV sets #35) In 2009, there were roughly 352,000 trademark applications filed in the United States. From these applications, about 320,000 trademarks were issued. What are the odds that a trademark application will result in a trademark being issued? Hint: consider a ratio of trademark applications that received approval to those applications that were denied. #36) A financial consultant estimates that there is an 11% chance a mutual fund will outperform the market during any given year. She also estimates that there is a 10% chance that the mutual fund will outperform the market for the next two years. What is the probability that the mutual fund will outperform the market in at least one of the next two years? #37) Three letters, with repetition allowed, are selected from the alphabet. What is the probability that none is repeated? #38) What is the probability that, in a group of 7 people, at least two are born in the same month?
8 8 #39) A jar contains 6 white marbles, 2 yellow marbles, 2 red marbles, and 5 blue marbles. Two marbles are picked at random and without replacement. a) What is the probability that both are blue? b) What is the probability that exactly one is blue? c) What is the probability that at least one is blue? Section 7.6 #40) Attendance at a football game in a certain city results in the following pattern. If it is extremely cold, the attendance will be 40,000; if it is cold, it will be 50,000; if it is moderate, 70,000, and if it is warm, 90,000. If the probability for extremely cold, cold, moderate, and warm are 0.09, 0.41, 0.41, 0.09, respectively, how many fans are expected to attend each game? #41) A player rolls a fair six-sided die and receives a number of dollars equal to the number of dots appearing on the face of the die. What is the least the player should expect to pay in order to play the game? #42) In a raffle, 1000 tickets are being sold at $1.00 each. The first prize is $110 dollars, and there are 4 second prizes of $50 dollars each. By how much does the price of a ticket exceed its expected value? #43) A 20-year old man purchases a one-year life insurance policy worth $250,000. The insurance company determines that he will survive the policy period with probability a) If the premium for the policy is $470, what is the expected profit for the insurance company? b) At what value should the company set its premium so its expected profit will be $220?
9 9 #44) A bag contains 2 red balls and 4 green ones. In a game, customers are charged $0.68 to draw two balls from the bag one after another without replacing them back. For each red ball that a customer draws, he or she is paid $1. Assuming that the order of drawing each ball matters, by how much will a customer overpay to play this game? #45) In a lottery, 1000 tickets are sold at $0.32 each. There are 3 cash prizes: one for $130, one for $80, and one for $10. Alice buys 7 tickets. A) Considering the expected value of each ticket, what would have been a fair price for a ticket? B) In total, how much extra did Alice pay? Section 8.1 #46) If E and F are events with P(E)=0.2 P(F)=0.3 ( ) a) Find P(E F) b) Find P(F E) c) Find ( ) #47) If E and F are events with ( ) and P(E F)=0.5 what is P(F)=?
10 10 #48) Given the following tree diagram probabilities, find the probability of obtaining D in any final outcome C 0.11 A 0.13 D 0.89 B 0.28 C 0.72 D #49) If P(E)=0.71 P(F)=0.79 ( ) find ( ) #50) If P(E)=0.20 P(F)=0.65 ( ) P(E F)=? [ ( ) ] #51) A regular deck of cards has 52 cards. There are 4 suits of 13 cards each. The suits are called Clubs (black), Diamonds (red), Hearts (red), and Spades (black). Two cards are drawn at random and without replacement from the deck. What is the probability that the first card is red and the second is black? #52) Given the data in the following table, what is the probability that a customer likes the deodorant given he/she is from group I? Like the deodorant Did not like the deodorant No opinion Group I Group II Group III
11 11 #53) If the probability that a store runs out of raspberry lemonade Gatorade when it is on sale is 0.84, and the probability the Gatorade is on sale is 0.21, what is the probability that Gatorade is on sale and the store runs out of the stock if the two events are independent of each other? Section 8.2 #54) Let E and F be independent events, P(E)=0.11 P(F)=0.35. What is ( ) #55) If E and F are independent, and if P(E)=0.3 and ( ), find P(F)=? #56) If E and F are independent and P(E)=0.40, ( ), find P(F)=? #57) If E and F are independent, with P(E)=0.5, P(F)=0.39 a) Find P(E F) b) Find P(F E) c) Find ( ) d) Find ( ) #58) If E, F, and G are independent events and P(E)=2/3 P(F)=3/13 P(G)=2/17 find ( ) #59) If P(E)=0.5 P(F)=0.3 ( ) find P(E F)
12 12 #60) A box has 10 marbles in it, two of these are red, and 8 are white. Suppose we draw a marble from the box, replace it, and then draw another. Find the probability that a) Both marbles are red b) Just one is red #61) A marksman hits a target with probability 0.6. Assuming independence for successive firings, find the probabilities of the following events: a) One miss followed by two hits. b) Two misses and one hit (in any order). Section 8.3 #62) Events and are mutually exclusive and form a complete partition of a sample space with ( ), ( ). If E is an event in with ( ) ( ), compute ( ) #63) Events,, and are mutually exclusive and form a complete partition of a sample space with ( ), ( ) ( ). If E is an event in with ( ) ( ), and ( ) compute ( ) #64) Events and are mutually exclusive and form a complete partition of a sample space with ( ), and ( ). If E is an event in ( ) and ( ), compute ( ) and ( ) [ ( ) ( ) ] #65) Events,, and are mutually exclusive and form a complete partition of a sample space with ( ), ( ) ( ). If E is an event in and ( ), ( ) and ( ). Compute ( ) ( ) and ( ) [ ( ) ( ) ( ) ]
(a) Fill in the missing probabilities in the table. (b) Calculate P(F G). (c) Calculate P(E c ). (d) Is this a uniform sample space?
Math 166 Exam 1 Review Sections L.1-L.2, 1.1-1.7 Note: This review is more heavily weighted on the new material this week: Sections 1.5-1.7. For more practice problems on previous material, take a look
More information4. Probability of an event A for equally likely outcomes:
University of California, Los Angeles Department of Statistics Statistics 110A Instructor: Nicolas Christou Probability Probability: A measure of the chance that something will occur. 1. Random experiment:
More informationEstadística I Exercises Chapter 4 Academic year 2015/16
Estadística I Exercises Chapter 4 Academic year 2015/16 1. An urn contains 15 balls numbered from 2 to 16. One ball is drawn at random and its number is reported. (a) Define the following events by listing
More informationUNIT 5 ~ Probability: What Are the Chances? 1
UNIT 5 ~ Probability: What Are the Chances? 1 6.1: Simulation Simulation: The of chance behavior, based on a that accurately reflects the phenomenon under consideration. (ex 1) Suppose we are interested
More informationIf S = {O 1, O 2,, O n }, where O i is the i th elementary outcome, and p i is the probability of the i th elementary outcome, then
1.1 Probabilities Def n: A random experiment is a process that, when performed, results in one and only one of many observations (or outcomes). The sample space S is the set of all elementary outcomes
More information7.5: Conditional Probability and Independent Events
c Dr Oksana Shatalov, Spring 2012 1 7.5: Conditional Probability and Independent Events EXAMPLE 1. Two cards are drawn from a deck of 52 without replacement. (a) What is the probability of that the first
More informationName: Exam 2 Solutions. March 13, 2017
Department of Mathematics University of Notre Dame Math 00 Finite Math Spring 07 Name: Instructors: Conant/Galvin Exam Solutions March, 07 This exam is in two parts on pages and contains problems worth
More informationExample. What is the sample space for flipping a fair coin? Rolling a 6-sided die? Find the event E where E = {x x has exactly one head}
Chapter 7 Notes 1 (c) Epstein, 2013 CHAPTER 7: PROBABILITY 7.1: Experiments, Sample Spaces and Events Chapter 7 Notes 2 (c) Epstein, 2013 What is the sample space for flipping a fair coin three times?
More informationChapter 8 Sequences, Series, and Probability
Chapter 8 Sequences, Series, and Probability Overview 8.1 Sequences and Series 8.2 Arithmetic Sequences and Partial Sums 8.3 Geometric Sequences and Partial Sums 8.5 The Binomial Theorem 8.6 Counting Principles
More information1. Consider the independent events A and B. Given that P(B) = 2P(A), and P(A B) = 0.52, find P(B). (Total 7 marks)
1. Consider the independent events A and B. Given that P(B) = 2P(A), and P(A B) = 0.52, find P(B). (Total 7 marks) 2. In a school of 88 boys, 32 study economics (E), 28 study history (H) and 39 do not
More informationIntermediate Math Circles November 8, 2017 Probability II
Intersection of Events and Independence Consider two groups of pairs of events Intermediate Math Circles November 8, 017 Probability II Group 1 (Dependent Events) A = {a sales associate has training} B
More informationMTH 201 Applied Mathematics Sample Final Exam Questions. 1. The augmented matrix of a system of equations (in two variables) is:
MTH 201 Applied Mathematics Sample Final Exam Questions 1. The augmented matrix of a system of equations (in two variables) is: 2 1 6 4 2 12 Which of the following is true about the system of equations?
More informationFall Math 140 Week-in-Review #5 courtesy: Kendra Kilmer (covering Sections 3.4 and 4.1) Section 3.4
Section 3.4 A Standard Maximization Problem has the following properties: The objective function is to be maximized. All variables are non-negative. Fall 2017 Math 140 Week-in-Review #5 courtesy: Kendra
More informationProbability and Statistics Notes
Probability and Statistics Notes Chapter One Jesse Crawford Department of Mathematics Tarleton State University (Tarleton State University) Chapter One Notes 1 / 71 Outline 1 A Sketch of Probability and
More informationTopic 5: Probability. 5.4 Combined Events and Conditional Probability Paper 1
Topic 5: Probability Standard Level 5.4 Combined Events and Conditional Probability Paper 1 1. In a group of 16 students, 12 take art and 8 take music. One student takes neither art nor music. The Venn
More informationMath 1313 Experiments, Events and Sample Spaces
Math 1313 Experiments, Events and Sample Spaces At the end of this recording, you should be able to define and use the basic terminology used in defining experiments. Terminology The next main topic in
More informationIntroduction to Probability
Introduction to Probability Content Experiments, Counting Rules, and Assigning Probabilities Events and Their Probability Some Basic Relationships of Probability Conditional Probability Bayes Theorem 2
More informationProbability the chance that an uncertain event will occur (always between 0 and 1)
Quantitative Methods 2013 1 Probability as a Numerical Measure of the Likelihood of Occurrence Probability the chance that an uncertain event will occur (always between 0 and 1) Increasing Likelihood of
More informationWeek 04 Discussion. a) What is the probability that of those selected for the in-depth interview 4 liked the new flavor and 1 did not?
STAT Wee Discussion Fall 7. A new flavor of toothpaste has been developed. It was tested by a group of people. Nine of the group said they lied the new flavor, and the remaining 6 indicated they did not.
More informationMath SL Day 66 Probability Practice [196 marks]
Math SL Day 66 Probability Practice [96 marks] Events A and B are independent with P(A B) = 0.2 and P(A B) = 0.6. a. Find P(B). valid interpretation (may be seen on a Venn diagram) P(A B) + P(A B), 0.2
More informationChapter 6. Probability
Chapter 6 robability Suppose two six-sided die is rolled and they both land on sixes. Or a coin is flipped and it lands on heads. Or record the color of the next 20 cars to pass an intersection. These
More information3 PROBABILITY TOPICS
Chapter 3 Probability Topics 135 3 PROBABILITY TOPICS Figure 3.1 Meteor showers are rare, but the probability of them occurring can be calculated. (credit: Navicore/flickr) Introduction It is often necessary
More informationELEG 3143 Probability & Stochastic Process Ch. 1 Probability
Department of Electrical Engineering University of Arkansas ELEG 3143 Probability & Stochastic Process Ch. 1 Probability Dr. Jingxian Wu wuj@uark.edu OUTLINE 2 Applications Elementary Set Theory Random
More informationPROBABILITY.
PROBABILITY PROBABILITY(Basic Terminology) Random Experiment: If in each trial of an experiment conducted under identical conditions, the outcome is not unique, but may be any one of the possible outcomes,
More informationBasic Concepts of Probability. Section 3.1 Basic Concepts of Probability. Probability Experiments. Chapter 3 Probability
Chapter 3 Probability 3.1 Basic Concepts of Probability 3.2 Conditional Probability and the Multiplication Rule 3.3 The Addition Rule 3.4 Additional Topics in Probability and Counting Section 3.1 Basic
More informationAxioms of Probability. Set Theory. M. Bremer. Math Spring 2018
Math 163 - pring 2018 Axioms of Probability Definition: The set of all possible outcomes of an experiment is called the sample space. The possible outcomes themselves are called elementary events. Any
More informationMidterm Review Honors ICM Name: Per: Remember to show work to receive credit! Circle your answers! Sets and Probability
Midterm Review Honors ICM Name: Per: Remember to show work to receive credit! Circle your answers! Unit 1 Sets and Probability 1. Let U denote the set of all the students at Green Hope High. Let D { x
More informationSouth Pacific Form Seven Certificate
141/1 South Pacific Form Seven Certificate INSTRUCTIONS MATHEMATICS WITH STATISTICS 2015 QUESTION and ANSWER BOOKLET Time allowed: Two and a half hours Write your Student Personal Identification Number
More informationDiscussion 03 Solutions
STAT Discussion Solutions Spring 8. A new flavor of toothpaste has been developed. It was tested by a group of people. Nine of the group said they liked the new flavor, and the remaining indicated they
More information3.2 Probability Rules
3.2 Probability Rules The idea of probability rests on the fact that chance behavior is predictable in the long run. In the last section, we used simulation to imitate chance behavior. Do we always need
More informationStat 225 Week 2, 8/27/12-8/31/12, Notes: Independence and Bayes Rule
Stat 225 Week 2, 8/27/12-8/31/12, Notes: Independence and Bayes Rule The Fall 2012 Stat 225 T.A.s September 7, 2012 1 Monday, 8/27/12, Notes on Independence In general, a conditional probability will change
More informationYear 10 Mathematics Probability Practice Test 1
Year 10 Mathematics Probability Practice Test 1 1 A letter is chosen randomly from the word TELEVISION. a How many letters are there in the word TELEVISION? b Find the probability that the letter is: i
More informationAlgebra EOC Practice Test #1
Class: Date: Algebra EOC Practice Test #1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. George is helping the manager of the local produce market expand
More information= 2 5 Note how we need to be somewhat careful with how we define the total number of outcomes in b) and d). We will return to this later.
PROBABILITY MATH CIRCLE (ADVANCED /27/203 The likelyhood of something (usually called an event happening is called the probability. Probability (informal: We can calculate probability using a ratio: want
More informationWeek 2. Section Texas A& M University. Department of Mathematics Texas A& M University, College Station 22 January-24 January 2019
Week 2 Section 1.2-1.4 Texas A& M University Department of Mathematics Texas A& M University, College Station 22 January-24 January 2019 Oğuz Gezmiş (TAMU) Topics in Contemporary Mathematics II Week2 1
More informationI - Probability. What is Probability? the chance of an event occuring. 1classical probability. 2empirical probability. 3subjective probability
What is Probability? the chance of an event occuring eg 1classical probability 2empirical probability 3subjective probability Section 2 - Probability (1) Probability - Terminology random (probability)
More informationAP Statistics Ch 6 Probability: The Study of Randomness
Ch 6.1 The Idea of Probability Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run. We call a phenomenon random if individual outcomes are uncertain
More informationCHAPTER 3 PROBABILITY TOPICS
CHAPTER 3 PROBABILITY TOPICS 1. Terminology In this chapter, we are interested in the probability of a particular event occurring when we conduct an experiment. The sample space of an experiment is the
More informationProblem # Number of points 1 /20 2 /20 3 /20 4 /20 5 /20 6 /20 7 /20 8 /20 Total /150
Name Student ID # Instructor: SOLUTION Sergey Kirshner STAT 516 Fall 09 Practice Midterm #1 January 31, 2010 You are not allowed to use books or notes. Non-programmable non-graphic calculators are permitted.
More informationRecord your answers and work on the separate answer sheet provided.
MATH 106 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually.
More informationProbabilistic models
Kolmogorov (Andrei Nikolaevich, 1903 1987) put forward an axiomatic system for probability theory. Foundations of the Calculus of Probabilities, published in 1933, immediately became the definitive formulation
More informationIndependence 1 2 P(H) = 1 4. On the other hand = P(F ) =
Independence Previously we considered the following experiment: A card is drawn at random from a standard deck of cards. Let H be the event that a heart is drawn, let R be the event that a red card is
More informationAssignment 2 SOLUTIONS
MATHEMATICS 01-10-LW Business Statistics Martin Huard Fall 00 Assignment SOLUTIONS This assignment is due on Friday September 6 at the beginning of the class. Question 1 ( points) In a marketing research,
More informationMath Fall 2010 Some Old Math 302 Exams There is always a danger when distributing old exams for a class that students will rely on them
Math 302.102 Fall 2010 Some Old Math 302 Exams There is always a danger when distributing old exams for a class that students will rely on them solely for their final exam preparations. The final exam
More informationMath Exam 1 Review. NOTE: For reviews of the other sections on Exam 1, refer to the first page of WIR #1 and #2.
Math 166 Fall 2008 c Heather Ramsey Page 1 Math 166 - Exam 1 Review NOTE: For reviews of the other sections on Exam 1, refer to the first page of WIR #1 and #2. Section 1.5 - Rules for Probability Elementary
More informationChapter. Probability
Chapter 3 Probability Section 3.1 Basic Concepts of Probability Section 3.1 Objectives Identify the sample space of a probability experiment Identify simple events Use the Fundamental Counting Principle
More informationCHAPTER 4 PROBABILITY AND PROBABILITY DISTRIBUTIONS
CHAPTER 4 PROBABILITY AND PROBABILITY DISTRIBUTIONS 4.2 Events and Sample Space De nition 1. An experiment is the process by which an observation (or measurement) is obtained Examples 1. 1: Tossing a pair
More informationHW MATH425/525 Lecture Notes 1
HW MATH425/525 Lecture Notes 1 Definition 4.1 If an experiment can be repeated under the same condition, its outcome cannot be predicted with certainty, and the collection of its every possible outcome
More information= A. Example 2. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {4, 6, 7, 9, 10}, and B = {2, 6, 8, 9}. Draw the sets on a Venn diagram.
MATH 109 Sets A mathematical set is a well-defined collection of objects A for which we can determine precisely whether or not any object belongs to A. Objects in a set are formally called elements of
More informationStat 225 Week 1, 8/20/12-8/24/12, Notes: Set Theory
Stat 225 Week 1, 8/20/12-8/24/12, Notes: Set Theory The Fall 2012 Stat 225 T.A.s September 7, 2012 The material in this handout is intended to cover general set theory topics. Information includes (but
More informationProbability Exercises. Problem 1.
Probability Exercises. Ma 162 Spring 2010 Ma 162 Spring 2010 April 21, 2010 Problem 1. ˆ Conditional Probability: It is known that a student who does his online homework on a regular basis has a chance
More informationMath 2311 Test 1 Review. 1. State whether each situation is categorical or quantitative. If quantitative, state whether it s discrete or continuous.
Math 2311 Test 1 Review Know all definitions! 1. State whether each situation is categorical or quantitative. If quantitative, state whether it s discrete or continuous. a. The amount a person grew (in
More informationAlgebra EOC Practice Test #1
Class: Date: Algebra EOC Practice Test #1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. George is helping the manager of the local produce market expand
More informationReview Counting Principles Theorems Examples. John Venn. Arthur Berg Counting Rules 2/ 21
Counting Rules John Venn Arthur Berg Counting Rules 2/ 21 Augustus De Morgan Arthur Berg Counting Rules 3/ 21 Algebraic Laws Let S be a sample space and A, B, C be three events in S. Commutative Laws:
More informationUNIT 5 INEQUALITIES CCM6+/7+ Name: Math Teacher:
UNIT 5 INEQUALITIES 2015-2016 CCM6+/7+ Name: Math Teacher: Topic(s) Page(s) Unit 5 Vocabulary 2 Writing and Graphing Inequalities 3 8 Solving One-Step Inequalities 9 15 Solving Multi-Step Inequalities
More informationName: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN. Mathematics 3201 PRE-PUBLIC EXAMINATION JUNE 2015
Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN Mathematics 3201 PRE-PUBLIC EXAMINATION JUNE 2015 Value: 100 Marks Duration: 3 Hours General Instructions
More informationConditional probability
CHAPTER 4 Conditional probability 4.1. Introduction Suppose there are 200 men, of which 100 are smokers, and 100 women, of which 20 are smokers. What is the probability that a person chosen at random will
More informationIntroduction to Probability Theory
Introduction to Probability Theory Overview The concept of probability is commonly used in everyday life, and can be expressed in many ways. For example, there is a 50:50 chance of a head when a fair coin
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MGF 1106 Math for Liberal Arts I Summer 2008 - Practice Final Exam Dr. Schnackenberg If you do not agree with the given answers, answer "E" for "None of the above". MULTIPLE CHOICE. Choose the one alternative
More informationChapter 5 : Probability. Exercise Sheet. SHilal. 1 P a g e
1 P a g e experiment ( observing / measuring ) outcomes = results sample space = set of all outcomes events = subset of outcomes If we collect all outcomes we are forming a sample space If we collect some
More informationSection 4.2 Basic Concepts of Probability
Section 4.2 Basic Concepts of Probability 2012 Pearson Education, Inc. All rights reserved. 1 of 88 Section 4.2 Objectives Identify the sample space of a probability experiment Identify simple events Use
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 informationSTAT 516: Basic Probability and its Applications
Lecture 3: Conditional Probability and Independence Prof. Michael September 29, 2015 Motivating Example Experiment ξ consists of rolling a fair die twice; A = { the first roll is 6 } amd B = { the sum
More information2.6 Tools for Counting sample points
2.6 Tools for Counting sample points When the number of simple events in S is too large, manual enumeration of every sample point in S is tedious or even impossible. (Example) If S contains N equiprobable
More informationMATH 1710 College Algebra Final Exam Review
MATH 1710 College Algebra Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) There were 480 people at a play.
More informationSTA 2023 EXAM-2 Practice Problems. Ven Mudunuru. From Chapters 4, 5, & Partly 6. With SOLUTIONS
STA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6 With SOLUTIONS Mudunuru, Venkateswara Rao STA 2023 Spring 2016 1 1. A committee of 5 persons is to be formed from 6 men and 4 women. What
More informationStudy Island. Scatter Plots
Study Island Copyright 2014 Edmentum - All rights reserved. 1. The table below shows the speed of a ball as it rolls down a slope. 3. David wondered if the temperature outside affects his gas He recorded
More informationProbabilistic models
Probabilistic models Kolmogorov (Andrei Nikolaevich, 1903 1987) put forward an axiomatic system for probability theory. Foundations of the Calculus of Probabilities, published in 1933, immediately became
More informationChapter 4 - Introduction to Probability
Chapter 4 - Introduction to Probability Probability is a numerical measure of the likelihood that an event will occur. Probability values are always assigned on a scale from 0 to 1. A probability near
More informationChapter 7: Section 7-1 Probability Theory and Counting Principles
Chapter 7: Section 7-1 Probability Theory and Counting Principles D. S. Malik Creighton University, Omaha, NE D. S. Malik Creighton University, Omaha, NE Chapter () 7: Section 7-1 Probability Theory and
More informationMath 119 Final Review version 1
Math 119 Final Review version 1 For problems 1 2, use inductive reasoning to find a pattern and then find the next number in the sequence. 1. 0, 3, 8, 15, 24, a. 33 b. 36 c. 35 d. 50 2.,,,, a. b. c. d.
More informationAxioms of Probability
Sample Space (denoted by S) The set of all possible outcomes of a random experiment is called the Sample Space of the experiment, and is denoted by S. Example 1.10 If the experiment consists of tossing
More informationConditional Probability
Conditional Probability Sometimes our computation of the probability of an event is changed by the knowledge that a related event has occurred (or is guaranteed to occur) or by some additional conditions
More informationCompound Events. The event E = E c (the complement of E) is the event consisting of those outcomes which are not in E.
Compound Events Because we are using the framework of set theory to analyze probability, we can use unions, intersections and complements to break complex events into compositions of events for which it
More informationTerm Definition Example Random Phenomena
UNIT VI STUDY GUIDE Probabilities Course Learning Outcomes for Unit VI Upon completion of this unit, students should be able to: 1. Apply mathematical principles used in real-world situations. 1.1 Demonstrate
More informationSTA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6. With SOLUTIONS
STA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6 With SOLUTIONS Mudunuru Venkateswara Rao, Ph.D. STA 2023 Fall 2016 Venkat Mu ALL THE CONTENT IN THESE SOLUTIONS PRESENTED IN BLUE AND BLACK
More information1. Determine whether each of the following stochastic matrices is a transition matrix for a Markov process that is regular, absorbing, or neither.
Math 166 Final Exam Review Note: This review does not cover every concept that could be tested on a final. Please also take a look at previous Week in Reviews for more practice problems. Every instructor
More informationNuevo examen - 02 de Febrero de 2017 [280 marks]
Nuevo examen - 0 de Febrero de 0 [0 marks] Jar A contains three red marbles and five green marbles. Two marbles are drawn from the jar, one after the other, without replacement. a. Find the probability
More informationPRACTICE EXAM UNIT #6: SYSTEMS OF LINEAR INEQUALITIES
_ School: Date: /45 SCAN OR FAX TO: Ms. Stamm (Central Collegiate) stamm.shelly@prairiesouth.ca FAX: (306) 692-6965 PH: (306) 693-4691 PRACTICE EXAM UNIT #6: SYSTEMS OF LINEAR INEQUALITIES Multiple Choice
More informationExam 2 Review (Sections Covered: 3.1, 3.3, , 7.1) Solutro. 1. Write a system of linear inequalities that describes the shaded region.
Exam 2 Review (Sections Covered: 31 33 6164 71) Solutro 1 Write a system of linear inequalities that describes the shaded region :) 5x +2y 30 x +2y " 2) 12 x : 0 y Z 0 : Line as 0 TO ± 30 True Line (2)
More informationMath 365 Final Exam Review Sheet. The final exam is Wednesday March 18 from 10am - 12 noon in MNB 110.
Math 365 Final Exam Review Sheet The final exam is Wednesday March 18 from 10am - 12 noon in MNB 110. The final is comprehensive and will cover Chapters 1, 2, 3, 4.1, 4.2, 5.2, and 5.3. You may use your
More informationOutline Conditional Probability The Law of Total Probability and Bayes Theorem Independent Events. Week 4 Classical Probability, Part II
Week 4 Classical Probability, Part II Week 4 Objectives This week we continue covering topics from classical probability. The notion of conditional probability is presented first. Important results/tools
More informationMath II Final Exam Question Bank Fall 2016
Math II Final Exam Question Bank Fall 2016 Name: Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which figure shows the flag on the left after it has been
More information1. Solve the following system of equations. 5x + y = 2z 13 3x + 3z = y 4y 2z = 2x + 12
Math 166 Final Exam Review Note: This review does not cover every concept that could be tested on a final. Please also take a look at previous Week in Reviews for more practice problems. Every instructor
More informationModule 1. Probability
Module 1 Probability 1. Introduction In our daily life we come across many processes whose nature cannot be predicted in advance. Such processes are referred to as random processes. The only way to derive
More information2.4. Conditional Probability
2.4. Conditional Probability Objectives. Definition of conditional probability and multiplication rule Total probability Bayes Theorem Example 2.4.1. (#46 p.80 textbook) Suppose an individual is randomly
More information2. Linda paid $38 for a jacket that was on sale for 25% of the original price. What was the original price of the jacket?
KCATM 011 Word Problems: Team 1. A restaurant s fixed price dinner includes an appetizer, an entrée, and dessert. If the restaurant offers 4 different types of appetizers, 5 different types of entrees,
More informationDate: Pd: Unit 4. GSE H Analytic Geometry EOC Review Name: Units Rewrite ( 12 3) 2 in simplest form. 2. Simplify
GSE H Analytic Geometry EOC Review Name: Units 4 7 Date: Pd: Unit 4 1. Rewrite ( 12 3) 2 in simplest form. 2. Simplify 18 25 3. Which expression is equivalent to 32 8? a) 2 2 27 4. Which expression is
More informationChance, too, which seems to rush along with slack reins, is bridled and governed by law (Boethius, ).
Chapter 2 Probability Chance, too, which seems to rush along with slack reins, is bridled and governed by law (Boethius, 480-524). Blaise Pascal (1623-1662) Pierre de Fermat (1601-1665) Abraham de Moivre
More informationProbability Experiments, Trials, Outcomes, Sample Spaces Example 1 Example 2
Probability Probability is the study of uncertain events or outcomes. Games of chance that involve rolling dice or dealing cards are one obvious area of application. However, probability models underlie
More informationNotes for Math 324, Part 17
126 Notes for Math 324, Part 17 Chapter 17 Common discrete distributions 17.1 Binomial Consider an experiment consisting by a series of trials. The only possible outcomes of the trials are success and
More information2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 3 Probability Contents 1. Events, Sample Spaces, and Probability 2. Unions and Intersections 3. Complementary Events 4. The Additive Rule and Mutually Exclusive
More informationTopic 3: Introduction to Probability
Topic 3: Introduction to Probability 1 Contents 1. Introduction 2. Simple Definitions 3. Types of Probability 4. Theorems of Probability 5. Probabilities under conditions of statistically independent events
More informationCHAPTER 3 PROBABILITY: EVENTS AND PROBABILITIES
CHAPTER 3 PROBABILITY: EVENTS AND PROBABILITIES PROBABILITY: A probability is a number between 0 and 1, inclusive, that states the long-run relative frequency, likelihood, or chance that an outcome will
More informationChapter Six. Approaches to Assigning Probabilities
Chapter Six Probability 6.1 Approaches to Assigning Probabilities There are three ways to assign a probability, P(O i ), to an outcome, O i, namely: Classical approach: based on equally likely events.
More informationMATH 556: PROBABILITY PRIMER
MATH 6: PROBABILITY PRIMER 1 DEFINITIONS, TERMINOLOGY, NOTATION 1.1 EVENTS AND THE SAMPLE SPACE Definition 1.1 An experiment is a one-off or repeatable process or procedure for which (a there is a well-defined
More informationMutually Exclusive Events
172 CHAPTER 3 PROBABILITY TOPICS c. QS, 7D, 6D, KS Mutually Exclusive Events A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes
More informationChapter 2 PROBABILITY SAMPLE SPACE
Chapter 2 PROBABILITY Key words: Sample space, sample point, tree diagram, events, complement, union and intersection of an event, mutually exclusive events; Counting techniques: multiplication rule, permutation,
More informationTOPIC 12 PROBABILITY SCHEMATIC DIAGRAM
TOPIC 12 PROBABILITY SCHEMATIC DIAGRAM Topic Concepts Degree of Importance References NCERT Book Vol. II Probability (i) Conditional Probability *** Article 1.2 and 1.2.1 Solved Examples 1 to 6 Q. Nos
More informationTopic 5 Part 3 [257 marks]
Topic 5 Part 3 [257 marks] Let 0 3 A = ( ) and 2 4 4 0 B = ( ). 5 1 1a. AB. 1b. Given that X 2A = B, find X. The following table shows the probability distribution of a discrete random variable X. 2a.
More information