Bayes stuff Red Cross and Blood Example

Size: px
Start display at page:

Download "Bayes stuff Red Cross and Blood Example"

Transcription

1 Bayes stuff Red Cross and Blood Example 42% of the workers at Motor Works are female, while 67% of the workers at City Bank are female. If one of these companies is selected at random (assume a chance for each), and then a worker is selected at random, what is the probability that the worker is female, if we know that the worker comes from City Bank? 14) Two shipments of components were received by a factory and stored in two separate bins. Shipment I has 2% of its contents defective, while shipment II has 5% of its contents defective. If it is equally likely an employee will go to either bin and select a component randomly, what is the probability that a defective component came from shipment II? ) A person must select one of three boxes, each filled with clocks. The probability of box A being selected is 0.31, of box B being selected is 0.13, and of box C being selected is The probability of finding a red clock in box A is 0.2, in box B is 0.4, and in box C is 0.9. A box is selected. Given that the box contains a red clock, what is the probability that box A was chosen? 16) In one town, 8% of year olds own a house, as do 28% of year olds and 52% of those over 50. According to a recent census taken in the town, 26.9% of adults in the town are years old, 36.0% are years old, and 37.1% are over 50. What percentage of house-owners are years old?

2 17) Among students at one college are 3934 women and 3103 men. The following table provides relative-frequency distributions for subject major for males and females at the college. Major Relative frequency for women Relative frequency for men Humanities Science Social Science Other A student is selected at random from the college. Determine the probability that the student selected is female given that he or she is a Humanities major ) The incidence of a certain disease in the town of Springwell is 4%. A new test has been developed to diagnose the disease. Using this test, 91% of those who have the disease test positive while 6% of those who do not have the disease test positive ("false positive"). If a person tests positive, what is the probability that he or she actually has the disease? Section 12.8 The Counting Principle and Permutations 2

3 Counting Principle If a first experiment can be performed in M distinct ways and a second experiment can be performed in N distinct ways, then the two experiments in that specific order can be performed in M N distinct ways A password is to consist of two lower case letters followed by four digits. Determine how many different passwords are possible if a) repetition of letters and digits is permitted. b) repetition of letters and digits is not permitted. c) the first letter must be a vowel, and the first digit cannot be a 0, and repetition of letters and digits is not permitted people, need 3 on a committee. They will be president, VP, and secretary. How many committees? Now all 13 on committee, again each with jobs

4 Example 3: Cell Phones In how many different ways can six different cell phones be arranged on top of one another? Consider the five letters a, b, c, d, e. In how many distinct ways can three letters be selected and arranged if repetition is not allowed? In how many different ways can the letters of the word BLINN be arranged? TALLAHASSEE MISSISSIPPI Seating Problems: We have 5 boys and 5 girls. In how many way can we seat them in a row if: 1) No restrictions 2) Alternate gender 3) Boys all together

5 We have 5 boys and 5 girls continued: Girls all together A girl on each end A boy on one end and a girl on the other NOT all of the girls next to each other Section 12.9 Combinations 13 people, need 3 on a committee. How many committees? Now all 13 on committee

6 7 red, 8 green marbles. We draw 4. How many ways to get: Exactly 1 red? Exactly 1 green? At least 2 red? red, 8 green, and 9 blue marbles. We draw 4. How many ways to get: Exactly 1 red? Exactly 1 green? At least 2 red? red, 8 green, and 9 blue marbles. We draw 4. How many ways to get: Exactly 2 red: Exactly 2 green: Exactly 2 red and exactly 2 green: Exactly 2 red or exactly 2 green:

7 Example 2: Museum Selection While visiting New York City, the Friedmans are interested in visiting 8 museums but have time to visit only 3. In how many ways can the Friedmans select 3 of the 8 museums to visit? Example 3: Floral Arrangements Jan Funkhauser has 10 different cut flowers from which she will choose 6 to use in a floral arrangement. How many different ways can she do so? Example 4: Dinner Combinations At the Royal Dynasty Chinese restaurant, dinner for eight people consists of 3 items from column A, 4 items from column B, and 3 items from column C. If columns A, B, and C have 5, 7, and 6 items, respectively, how many different dinner combinations are possible?

8 How many 5 card hands: Total? Have at least 3 Kings? Have at least 3 spades? Have at least 1 heart? Have 3 spades and 2 hearts? Have of one suit and 2 of another? Section Solving Probability Problems by Using Combinations Example 1: Committee of Three Women A club consists of four men and five women. Three members are to be selected at random to form a committee. What is the probability that the committee will consist of three women?

9 25 Example 5: Rare Coins Conner Shanahan s rare coin collection is made up of 8 silver dollars, 7 quarters, and 5 dimes. Conner plans to sell 8 of his 20 coins to finance part of his college education. If he selects the coins at random, what is the probability that 3 silver dollars, 2 quarters, and 3 dimes are selected? A temporary agency has six men and five women who wish to be assigned for the day. One employer has requested four employees for security guard positions, and the second employer has requested three employees for moving furniture in an office building. If we assume that each of the potential employees has the same chance of being selected and being assigned at random and that only seven employees will be assigned, find the probability that a) three men will be selected for moving furniture. b) three men will be selected for moving furniture and four women will be selected for security guard positions Section Binomial Probability Formula 9

10 To Use the Binomial Probability Formula There are n repeated independent trials. Each trial has two possible outcomes, success and failure. For each trial, the probability of success (and failure) remains the same. Binomial Probability Formula The probability of obtaining exactly x successes, P(x), in n independent trials is given by: P( x)= ( n C x )p x q n x where p is the probability of success on a single trial and q (= 1 p) is the probability of failure on a single trial. A basket contains 3 balls: 1 red, 1 blue, and 1 yellow. Three balls are going to be selected from the basket. Find the probability that a. no red balls are selected if we draw without replacement b. no red balls are selected if we draw with replacement

11 A basket contains 1 red, 1 blue, and 1 yellow. Three balls are going to be selected from the basket with replacement. Find the probability: exactly 1 red ball is selected. exactly 2 red balls are selected. exactly 3 red balls are selected. Example 4: Planting Trees The probability that a tree planted by a landscaping company will survive is 0.8. If they plant four determine the probability that a) none will survive. b) at least one will survive. c) At least two will survive The Dr. Pepper says 1 in 8 wins. If you buy 20 of those drinks this semester, find the probability (A) you win at least twice: (B) You do not win at all: (C) You win fewer than three times: (D) For the class, how many of A,B,C would we expect? 11

12 In one city, the probability that a person will pass his or her driving test on the first attempt is people are selected at random from among those taking their driving test for the first time. What is the probability that: The number passing is less than 4? The number passing is more than 10? The number passing is between 2 and 8 (inclusive)? 41% of the murder trials in one district result in a guilty verdict. Five murder trials are selected at random from the district. Determine the probability distribution of X, the number of trials among the five selected in which the defendant is found guilty. A multiple choice test consists of four questions. Each question has five possible answers of which only one is correct. A student guesses on every question. Find the probability distribution of X, the number of questions she answers correctly. Copyrig ht 12

Name: 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

Name: 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 information

Section The Multiplication Principle and Permutations

Section The Multiplication Principle and Permutations Section 2.1 - The Multiplication Principle and Permutations Example 1: A yogurt shop has 4 flavors (chocolate, vanilla, strawberry, and blueberry) and three sizes (small, medium, and large). How many different

More information

Finite Mathematics MAT 141: Chapter 8 Notes

Finite Mathematics MAT 141: Chapter 8 Notes Finite Mathematics MAT 4: Chapter 8 Notes Counting Principles; More David J. Gisch The Multiplication Principle; Permutations Multiplication Principle Multiplication Principle You can think of the multiplication

More information

Q1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together.

Q1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together. Required Probability = where Q1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together. Solution: As girls are always together so they are considered as a group.

More information

Review Questions on Ch4 and Ch5

Review 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 information

CISC 1400 Discrete Structures

CISC 1400 Discrete Structures CISC 1400 Discrete Structures Chapter 6 Counting CISC1400 Yanjun Li 1 1 New York Lottery New York Mega-million Jackpot Pick 5 numbers from 1 56, plus a mega ball number from 1 46, you could win biggest

More information

Applied Statistics I

Applied Statistics I Applied Statistics I Liang Zhang Department of Mathematics, University of Utah June 12, 2008 Liang Zhang (UofU) Applied Statistics I June 12, 2008 1 / 29 In Probability, our main focus is to determine

More information

3 The multiplication rule/miscellaneous counting problems

3 The multiplication rule/miscellaneous counting problems Practice for Exam 1 1 Axioms of probability, disjoint and independent events 1 Suppose P (A 0, P (B 05 (a If A and B are independent, what is P (A B? What is P (A B? (b If A and B are disjoint, what is

More information

Unit 9: Probability Assignments

Unit 9: Probability Assignments Unit 9: Probability Assignments #1: Basic Probability In each of exercises 1 & 2, find the probability that the spinner shown would land on (a) red, (b) yellow, (c) blue. 1. 2. Y B B Y B R Y Y B R 3. Suppose

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. 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 information

Section 5.4 Permutations and Combinations

Section 5.4 Permutations and Combinations Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to

More information

Probability and Counting Techniques

Probability 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 information

Section 5.4 Permutations and Combinations

Section 5.4 Permutations and Combinations Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! = n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to

More information

3 The multiplication rule/miscellaneous counting problems

3 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 information

Math 227 Elementary Statistics. Bluman 5 th edition

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 information

Counting (Enumerative Combinatorics) X. Zhang, Fordham Univ.

Counting (Enumerative Combinatorics) X. Zhang, Fordham Univ. Counting (Enumerative Combinatorics) X. Zhang, Fordham Univ. 1 Chance of winning?! What s the chances of winning New York Megamillion Jackpot!! just pick 5 numbers from 1 to 56, plus a mega ball number

More information

MAT104: Fundamentals of Mathematics II Summary of Counting Techniques and Probability. Preliminary Concepts, Formulas, and Terminology

MAT104: Fundamentals of Mathematics II Summary of Counting Techniques and Probability. Preliminary Concepts, Formulas, and Terminology MAT104: Fundamentals of Mathematics II Summary of Counting Techniques and Probability Preliminary Concepts, Formulas, and Terminology Meanings of Basic Arithmetic Operations in Mathematics Addition: Generally

More information

Fundamental Counting Principle

Fundamental Counting Principle Lesson 88 Probability with Combinatorics HL2 Math - Santowski Fundamental Counting Principle Fundamental Counting Principle can be used determine the number of possible outcomes when there are two or more

More information

Math 1342 Exam 2 Review

Math 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 information

Math 12 Academic Assignment 9: Probability Outcomes: B8, G1, G2, G3, G4, G7, G8

Math 12 Academic Assignment 9: Probability Outcomes: B8, G1, G2, G3, G4, G7, G8 Math 12 Academic Assignment 9: Probability Outcomes: B8, G1, G2, G3, G4, G7, G8 Name: 45 1. A customer chooses 5 or 6 tapes from a bin of 40. What is the expression that gives the total number of possibilities?

More information

Name: Spring P. Walston/A. Moore. Topic worksheet # assigned #completed Teacher s Signature Tree Diagrams FCP

Name: Spring P. Walston/A. Moore. Topic worksheet # assigned #completed Teacher s Signature Tree Diagrams FCP Name: Spring 2016 P. Walston/A. Moore Topic worksheet # assigned #completed Teacher s Signature Tree Diagrams 1-0 13 FCP 1-1 16 Combinations/ Permutations Factorials 1-2 22 1-3 20 Intro to Probability

More information

Fundamentals of Probability

Fundamentals 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 information

Examples: Experiment Sample space

Examples: Experiment Sample space Intro to Probability: A cynical person once said, The only two sure things are death and taxes. This philosophy no doubt arose because so much in people s lives is affected by chance. From the time a person

More information

6. In how many different ways can you answer 10 multiple-choice questions if each question has five choices?

6. In how many different ways can you answer 10 multiple-choice questions if each question has five choices? Pre-Calculus Section 4.1 Multiplication, Addition, and Complement 1. Evaluate each of the following: a. 5! b. 6! c. 7! d. 0! 2. Evaluate each of the following: a. 10! b. 20! 9! 18! 3. In how many different

More information

Class XII Chapter 13 Probability Maths. Exercise 13.1

Class 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 information

Chapter 2. Permutations and Combinations

Chapter 2. Permutations and Combinations 2. Permutations and Combinations Chapter 2. Permutations and Combinations In this chapter, we define sets and count the objects in them. Example Let S be the set of students in this classroom today. Find

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) 1 6

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) 1 6 Math 300 Exam 4 Review (Chapter 11) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Give the probability that the spinner shown would land on

More information

Axiomatic Probability

Axiomatic Probability Axiomatic Probability The objective of probability is to assign to each event A a number P(A), called the probability of the event A, which will give a precise measure of the chance thtat A will occur.

More information

Chapter 11: Probability and Counting Techniques

Chapter 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 information

Week in Review #5 ( , 3.1)

Week in Review #5 ( , 3.1) Math 166 Week-in-Review - S. Nite 10/6/2012 Page 1 of 5 Week in Review #5 (2.3-2.4, 3.1) n( E) In general, the probability of an event is P ( E) =. n( S) Distinguishable Permutations Given a set of n objects

More information

50 Counting Questions

50 Counting Questions 50 Counting Questions Prob-Stats (Math 3350) Fall 2012 Formulas and Notation Permutations: P (n, k) = n!, the number of ordered ways to permute n objects into (n k)! k bins. Combinations: ( ) n k = n!,

More information

Name: Section: Date:

Name: Section: Date: WORKSHEET 5: PROBABILITY Name: Section: Date: Answer the following problems and show computations on the blank spaces provided. 1. In a class there are 14 boys and 16 girls. What is the probability of

More information

CHAPTER 8 Additional Probability Topics

CHAPTER 8 Additional Probability Topics CHAPTER 8 Additional Probability Topics 8.1. Conditional Probability Conditional probability arises in probability experiments when the person performing the experiment is given some extra information

More information

Probability Review 41

Probability 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 information

Introduction. Firstly however we must look at the Fundamental Principle of Counting (sometimes referred to as the multiplication rule) which states:

Introduction. Firstly however we must look at the Fundamental Principle of Counting (sometimes referred to as the multiplication rule) which states: Worksheet 4.11 Counting Section 1 Introduction When looking at situations involving counting it is often not practical to count things individually. Instead techniques have been developed to help us count

More information

4.1 Sample Spaces and Events

4.1 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 information

Probability Concepts and Counting Rules

Probability Concepts and Counting Rules Probability Concepts and Counting Rules Chapter 4 McGraw-Hill/Irwin Dr. Ateq Ahmed Al-Ghamedi Department of Statistics P O Box 80203 King Abdulaziz University Jeddah 21589, Saudi Arabia ateq@kau.edu.sa

More information

Chapter 3: Elements of Chance: Probability Methods

Chapter 3: Elements of Chance: Probability Methods Chapter 3: Elements of Chance: Methods Department of Mathematics Izmir University of Economics Week 3-4 2014-2015 Introduction In this chapter we will focus on the definitions of random experiment, outcome,

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. 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 information

Honors Precalculus Chapter 9 Summary Basic Combinatorics

Honors Precalculus Chapter 9 Summary Basic Combinatorics Honors Precalculus Chapter 9 Summary Basic Combinatorics A. Factorial: n! means 0! = Why? B. Counting principle: 1. How many different ways can a license plate be formed a) if 7 letters are used and each

More information

Algebra II- Chapter 12- Test Review

Algebra II- Chapter 12- Test Review Sections: Counting Principle Permutations Combinations Probability Name Choose the letter of the term that best matches each statement or phrase. 1. An illustration used to show the total number of A.

More information

Spring 2016 Math 54 Test #2 Name: Write your work neatly. You may use TI calculator and formula sheet. Total points: 103

Spring 2016 Math 54 Test #2 Name: Write your work neatly. You may use TI calculator and formula sheet. Total points: 103 Spring 2016 Math 54 Test #2 Name: Write your work neatly. You may use TI calculator and formula sheet. Total points: 103 1. (8) The following are amounts of time (minutes) spent on hygiene and grooming

More information

Section : Combinations and Permutations

Section : Combinations and Permutations Section 11.1-11.2: Combinations and Permutations Diana Pell A construction crew has three members. A team of two must be chosen for a particular job. In how many ways can the team be chosen? How many words

More information

MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING DR. DAVID BRIDGE

MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING DR. DAVID BRIDGE MATH 2053 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING 2009 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the

More information

Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +]

Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +] Math 3201 Assignment 1 of 1 Unit 2 Counting Methods Name: Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +] Identify the choice that best completes the statement or answers the question. 1.

More information

Name Date Trial 1: Capture distances with only decimeter markings. Name Trial 1 Trial 2 Trial 3 Average

Name Date Trial 1: Capture distances with only decimeter markings. Name Trial 1 Trial 2 Trial 3 Average Decimal Drop Name Date Trial 1: Capture distances with only decimeter markings. Name Trial 1 Trial 2 Trial 3 Average Trial 2: Capture distances with centimeter markings Name Trial 1 Trial 2 Trial 3 Average

More information

Exam 2 Review (Sections Covered: 3.1, 3.3, , 7.1) 1. Write a system of linear inequalities that describes the shaded region.

Exam 2 Review (Sections Covered: 3.1, 3.3, , 7.1) 1. Write a system of linear inequalities that describes the shaded region. Exam 2 Review (Sections Covered: 3.1, 3.3, 6.1-6.4, 7.1) 1. Write a system of linear inequalities that describes the shaded region. 5x + 2y 30 x + 2y 12 x 0 y 0 2. Write a system of linear inequalities

More information

Conditional Probability Worksheet

Conditional Probability Worksheet Conditional Probability Worksheet EXAMPLE 4. Drug Testing and Conditional Probability Suppose that a company claims it has a test that is 95% effective in determining whether an athlete is using a steroid.

More information

, -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.

, -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. 4-1 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,

More information

where n is the number of distinct objects and r is the number of distinct objects taken r at a time.

where n is the number of distinct objects and r is the number of distinct objects taken r at a time. Section 5.4: Permutations and Combinations Definition: n-factorial For any natural number n, nn(nn 1)(nn 2) 3 2 1 0! = 1 A permutation is an arrangement of a specific set where the order in which the objects

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. More 9.-9.3 Practice Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. ) In how many ways can you answer the questions on

More information

Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +]

Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +] Math 3201 Assignment 2 Unit 2 Counting Methods Name: Fundamental Counting Principle 2.1 Page 66 [And = *, Or = +] Identify the choice that best completes the statement or answers the question. Show all

More information

Chapter 5 Probability

Chapter 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 information

6.1.1 The multiplication rule

6.1.1 The multiplication rule 6.1.1 The multiplication rule 1. There are 3 routes joining village A and village B and 4 routes joining village B and village C. Find the number of different ways of traveling from village A to village

More information

Homework Set #1. 1. The Supreme Court (9 members) meet, and all the justices shake hands with each other. How many handshakes are there?

Homework Set #1. 1. The Supreme Court (9 members) meet, and all the justices shake hands with each other. How many handshakes are there? Homework Set # Part I: COMBINATORICS (follows Lecture ). The Supreme Court (9 members) meet, and all the justices shake hands with each other. How many handshakes are there? 2. A country has license plates

More information

MATH 1115, Mathematics for Commerce WINTER 2011 Toby Kenney Homework Sheet 6 Model Solutions

MATH 1115, Mathematics for Commerce WINTER 2011 Toby Kenney Homework Sheet 6 Model Solutions MATH, Mathematics for Commerce WINTER 0 Toby Kenney Homework Sheet Model Solutions. A company has two machines for producing a product. The first machine produces defective products % of the time. The

More information

1 2-step and other basic conditional probability problems

1 2-step and other basic conditional probability problems Name M362K Exam 2 Instructions: Show all of your work. You do not have to simplify your answers. No calculators allowed. 1 2-step and other basic conditional probability problems 1. Suppose A, B, C are

More information

Chapter 11: Probability and Counting Techniques

Chapter 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 two-letter words (including nonsense words) can be formed when

More information

Unit 5 Radical Functions & Combinatorics

Unit 5 Radical Functions & Combinatorics 1 Unit 5 Radical Functions & Combinatorics General Outcome: Develop algebraic and graphical reasoning through the study of relations. Develop algebraic and numeric reasoning that involves combinatorics.

More information

The point value of each problem is in the left-hand margin. You must show your work to receive any credit, except on problems 1 & 2. Work neatly.

The point value of each problem is in the left-hand 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 5-7 4 Problem Pages 4 Formula/Table Pages Time Limit: 90 Minutes 1 No Scratch Paper Calculator Allowed: Scientific Name: The point value of

More information

Chapter 6 -- Probability Review Questions

Chapter 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 information

Finite Math B, Chapter 8 Test Review Name

Finite Math B, Chapter 8 Test Review Name Finite Math B, Chapter 8 Test Review Name Evaluate the factorial. 1) 6! A) 720 B) 120 C) 360 D) 1440 Evaluate the permutation. 2) P( 10, 5) A) 10 B) 30,240 C) 1 D) 720 3) P( 12, 8) A) 19,958,400 B) C)

More information

Instructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include your name and student ID.

Instructions: 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 information

Chapter 3: PROBABILITY

Chapter 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 information

4.1 What is Probability?

4.1 What is Probability? 4.1 What is Probability? between 0 and 1 to indicate the likelihood of an event. We use event is to occur. 1 use three major methods: 1) Intuition 3) Equally Likely Outcomes Intuition - prediction based

More information

Solutions - Problems in Probability (Student Version) Section 1 Events, Sample Spaces and Probability. 1. If three coins are flipped, the outcomes are

Solutions - Problems in Probability (Student Version) Section 1 Events, Sample Spaces and Probability. 1. If three coins are flipped, the outcomes are Solutions - Problems in Probability (Student Version) Section 1 Events, Sample Spaces and Probability 1. If three coins are flipped, the outcomes are HTT,HTH,HHT,HHH,TTT,TTH,THT,THH. There are eight outcomes.

More information

1 2-step and other basic conditional probability problems

1 2-step and other basic conditional probability problems Name M362K Exam 2 Instructions: Show all of your work. You do not have to simplify your answers. No calculators allowed. 1 2-step and other basic conditional probability problems 1. Suppose A, B, C are

More information

Probability Test Review Math 2. a. What is? b. What is? c. ( ) d. ( )

Probability Test Review Math 2. a. What is? b. What is? c. ( ) d. ( ) Probability Test Review Math 2 Name 1. Use the following venn diagram to answer the question: Event A: Odd Numbers Event B: Numbers greater than 10 a. What is? b. What is? c. ( ) d. ( ) 2. In Jason's homeroom

More information

Unit on Permutations and Combinations (Counting Techniques)

Unit on Permutations and Combinations (Counting Techniques) Page 1 of 15 (Edit by Y.M. LIU) Page 2 of 15 (Edit by Y.M. LIU) Unit on Permutations and Combinations (Counting Techniques) e.g. How many different license plates can be made that consist of three digits

More information

Conditional Probability Worksheet

Conditional Probability Worksheet Conditional Probability Worksheet P( A and B) P(A B) = P( B) Exercises 3-6, 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 information

PROBABILITY. 1. Introduction. Candidates should able to:

PROBABILITY. 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 information

MATH 215 DISCRETE MATHEMATICS INSTRUCTOR: P. WENG

MATH 215 DISCRETE MATHEMATICS INSTRUCTOR: P. WENG MATH DISCRETE MATHEMATICS INSTRUCTOR: P. WENG Counting and Probability Suggested Problems Basic Counting Skills, Inclusion-Exclusion, and Complement. (a An office building contains 7 floors and has 7 offices

More information

Most of the time we deal with theoretical probability. Experimental probability uses actual data that has been collected.

Most of the time we deal with theoretical probability. Experimental probability uses actual data that has been collected. AFM Unit 7 Day 3 Notes Theoretical vs. Experimental Probability Name Date Definitions: Experiment: process that gives a definite result Outcomes: results Sample space: set of all possible outcomes Event:

More information

Independent Events. If we were to flip a coin, each time we flip that coin the chance of it landing on heads or tails will always remain the same.

Independent Events. If we were to flip a coin, each time we flip that coin the chance of it landing on heads or tails will always remain the same. Independent Events Independent events are events that you can do repeated trials and each trial doesn t have an effect on the outcome of the next trial. If we were to flip a coin, each time we flip that

More information

Math 1101 Combinations Handout #17

Math 1101 Combinations Handout #17 Math 1101 Combinations Handout #17 1. Compute the following: (a) C(8, 4) (b) C(17, 3) (c) C(20, 5) 2. In the lottery game Megabucks, it used to be that a person chose 6 out of 36 numbers. The order of

More information

Study Island Statistics and Probability

Study Island Statistics and Probability Study Island Statistics and Probability Copyright 2014 Edmentum - All rights reserved. 1. An experiment is broken up into two parts. In the first part of the experiment, a six-sided die is rolled. In the

More information

Advanced Intermediate Algebra Chapter 12 Summary INTRO TO PROBABILITY

Advanced Intermediate Algebra Chapter 12 Summary INTRO TO PROBABILITY Advanced Intermediate Algebra Chapter 12 Summary INTRO TO PROBABILITY 1. Jack and Jill do not like washing dishes. They decide to use a random method to select whose turn it is. They put some red and blue

More information

November 11, Chapter 8: Probability: The Mathematics of Chance

November 11, Chapter 8: Probability: The Mathematics of Chance Chapter 8: Probability: The Mathematics of Chance November 11, 2013 Last Time Probability Models and Rules Discrete Probability Models Equally Likely Outcomes Probability Rules Probability Rules Rule 1.

More information

Section 6.4 Permutations and Combinations: Part 1

Section 6.4 Permutations and Combinations: Part 1 Section 6.4 Permutations and Combinations: Part 1 Permutations 1. How many ways can you arrange three people in a line? 2. Five people are waiting to take a picture. How many ways can you arrange three

More information

Using a table: regular fine micro. red. green. The number of pens possible is the number of cells in the table: 3 2.

Using a table: regular fine micro. red. green. The number of pens possible is the number of cells in the table: 3 2. Counting Methods: Example: A pen has tip options of regular tip, fine tip, or micro tip, and it has ink color options of red ink or green ink. How many different pens are possible? Using a table: regular

More information

Contents 2.1 Basic Concepts of Probability Methods of Assigning Probabilities Principle of Counting - Permutation and Combination 39

Contents 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 information

Counting Methods and Probability

Counting Methods and Probability CHAPTER Counting Methods and Probability Many good basketball players can make 90% of their free throws. However, the likelihood of a player making several free throws in a row will be less than 90%. You

More information

D1 Probability of One Event

D1 Probability of One Event D Probability of One Event Year 3/4. I have 3 bags of marbles. Bag A contains 0 marbles, Bag B contains 20 marbles and Bag C contains 30 marbles. One marble in each bag is red. a) Join up each statement

More information

LC OL Probability. ARNMaths.weebly.com. As part of Leaving Certificate Ordinary Level Math you should be able to complete the following.

LC OL Probability. ARNMaths.weebly.com. As part of Leaving Certificate Ordinary Level Math you should be able to complete the following. A Ryan LC OL Probability ARNMaths.weebly.com Learning Outcomes As part of Leaving Certificate Ordinary Level Math you should be able to complete the following. Counting List outcomes of an experiment Apply

More information

Created by T. Madas COMBINATORICS. Created by T. Madas

Created by T. Madas COMBINATORICS. Created by T. Madas COMBINATORICS COMBINATIONS Question 1 (**) The Oakwood Jogging Club consists of 7 men and 6 women who go for a 5 mile run every Thursday. It is decided that a team of 8 runners would be picked at random

More information

Exam III Review Problems

Exam 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 Week-in-Reviews

More information

Raise your hand if you rode a bus within the past month. Record the number of raised hands.

Raise 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 information

4.4: The Counting Rules

4.4: The Counting Rules 4.4: The Counting Rules The counting rules can be used to discover the number of possible for a sequence of events. Fundamental Counting Rule In a sequence of n events in which the first one has k 1 possibilities

More information

Math 1313 Section 6.2 Definition of Probability

Math 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 information

CHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY

CHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY CHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY Probability is the Probability is used in many real-world fields, such as insurance, medical research, law enforcement, and political science. Objectives:

More information

Counting Principles Review

Counting Principles Review Counting Principles Review 1. A magazine poll sampling 100 people gives that following results: 17 read magazine A 18 read magazine B 14 read magazine C 8 read magazines A and B 7 read magazines A and

More information

Math 4610, Problems to be Worked in Class

Math 4610, Problems to be Worked in Class Math 4610, Problems to be Worked in Class Bring this handout to class always! You will need it. If you wish to use an expanded version of this handout with space to write solutions, you can download one

More information

COMBINATORIAL PROBABILITY

COMBINATORIAL PROBABILITY COMBINATORIAL PROBABILITY Question 1 (**+) The Oakwood Jogging Club consists of 7 men and 6 women who go for a 5 mile run every Thursday. It is decided that a team of 8 runners would be picked at random

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 Practice Test 2 Ch 4 & 5 Name 1) Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. 1) List the outcomes

More information

April 10, ex) Draw a tree diagram of this situation.

April 10, ex) Draw a tree diagram of this situation. April 10, 2014 12-1 Fundamental Counting Principle & Multiplying Probabilities 1. Outcome - the result of a single trial. 2. Sample Space - the set of all possible outcomes 3. Independent Events - when

More information

North Seattle Community College Winter ELEMENTARY STATISTICS 2617 MATH Section 05, Practice Questions for Test 2 Chapter 3 and 4

North 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 information

STAT Statistics I Midterm Exam One. Good Luck!

STAT Statistics I Midterm Exam One. Good Luck! STAT 515 - Statistics I Midterm Exam One Name: Instruction: You can use a calculator that has no connection to the Internet. Books, notes, cellphones, and computers are NOT allowed in the test. There are

More information

Math 1 Unit 4 Mid-Unit Review Chances of Winning

Math 1 Unit 4 Mid-Unit Review Chances of Winning Math 1 Unit 4 Mid-Unit Review Chances of Winning Name My child studied for the Unit 4 Mid-Unit Test. I am aware that tests are worth 40% of my child s grade. Parent Signature MM1D1 a. Apply the addition

More information

Introduction to Mathematical Reasoning, Saylor 111

Introduction to Mathematical Reasoning, Saylor 111 Here s a game I like plying with students I ll write a positive integer on the board that comes from a set S You can propose other numbers, and I tell you if your proposed number comes from the set Eventually

More information

Empirical (or statistical) probability) is based on. The empirical probability of an event E is the frequency of event E.

Empirical (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 3-1 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 information