# 19.4 Mutually Exclusive and Overlapping Events

Size: px
Start display at page:

Transcription

1 Name Class Date 19.4 Mutually Exclusive and Overlapping Events Essential Question: How are probabilities affected when events are mutually exclusive or overlapping? Resource Locker Explore 1 Finding the Probability of Mutually Exclusive Events Two events are mutually exclusive events if they cannot both occur in the same trial of an experiment. For example, if you flip a coin it cannot land heads up and tails up in the same trial. Therefore, the events are mutually exclusive. A number dodecahedron has 12 sides numbered 1 through 12. What is the probability that you roll the cube and the result is an even number or a 7? A Let A be the event that you roll an even number. Let B be the event that you roll a 7. Let S be the sample space. Complete the Venn diagram by writing all outcomes in the sample space in the appropriate region. S A B B D Calculate P (A). P (A) = _ = _ Calculate P (A or B). n (S) = n (A or B) = n (A) + n (B) = + = C E Calculate P (B). P (B) = _ Calculate P (A) + P (B). Compare the answer to Step D. P (A) + P (B) = _ + _ = _ n (A or B) So, P (A or B) = _ = _. n (S) P (A) + P (B) P (A or B). Module Lesson 4

2 Reflect 1. Discussion How would you describe mutually exclusive events to another student in your own words? How could you use a Venn diagram to assist in your explanation? 2. Look back over the steps. What can you conjecture about the probability of the union of events that are mutually exclusive? Explore 2 Finding the Probability of Overlapping Events The process used in the previous Explore can be generalized to give the formula for the probability of mutually exclusive events. Mutually Exclusive Events If A and B are mutually exclusive events, then P (A or B) = P (A) + P (B). Two events are overlapping events (or inclusive events) if they have one or more outcomes in common. What is the probability that you roll a number dodecahedron and the result is an even number or a number greater than 7? A Let A be the event that you roll an even number. Let B be the event that you roll a number greater than 7. Let S be the sample space. Complete the Venn diagram by writing all outcomes in the sample space in the appropriate region. S A B Module Lesson 4

3 B Calculate P (A). C Calculate P (B). P (A) = _ = _ P (B) = _ D Calculate P (A and B). P (A and B) = _ = _ E Use the Venn diagram to find P (A or B). P (A or B) = _ = _ Now, use P (A), P (B), and P (A and B) to calculate P (A or B). P (A) = P (B) = P (A and B) = P (A) + P (B) - P (A and B) = + - = Reflect 3. Why must you subtract P (A and B) from P (A) + P (B) to determine P (A or B)? 4. Look back over the steps. What can you conjecture about the probability of the union of two events that are overlapping? Explain 1 Finding a Probability From a Two-Way Table of Data The previous Explore leads to the following rule. The Addition Rule P (A or B) = P (A) + P (B) - P (A and B) Example 1 Use the given two-way tables to determine the probabilities. A P (senior or girl) Freshman Sophomore Junior Senior TOTAL Boy Girl Total To determine P (senior or girl), first calculate P (senior), P (girl), and P (senior and girl). Module Lesson 4

4 _ 202 P (senior) = 808 = 1_ 4 ; P (girl) = _ = _ Use the addition rule to determine P (senior or girl). P (senior and girl) = _ = _ P (senior or girl) = P (senior) + P (girl) - P (senior and girl) = 1_ 4 + _ _ = _ Therefore, the probability that a student is a senior or a girl is _ B P ( (domestic or late) c ) Domestic Flights International Flights Late On Time Total Total To determine P ( (domestic or late) c ), first calculate P (domestic or late). P (domestic) = _ = _ ; P (late) = _ = _ ; P (domestic and late) = _ = _ Use the addition rule to determine P (domestic or late). P (domestic or late) = P (domestic) + P (late) - P (domestic and late) = _ + _ - _ = _ Therefore, P ( (domestic or late) c ) = 1 - P (domestic or late) = 1 - _ = _ Image Credits: Elena Elisseeva/Cutcaster Module Lesson 4

5 Your Turn 5. Use the table to determine P (headache or no medicine). Took Medicine No Medicine TOTAL Headache No Headache TOTAL Elaborate 6. Give an example of mutually exclusive events and an example of overlapping events. 7. Essential Question Check-In How do you determine the probability of mutually exclusive events and overlapping events? Evaluate: Homework and Practice 1. A bag contains 3 blue marbles, 5 red marbles, and 4 green marbles. You choose one without looking. What is the probability that it is red or green? Online Homework Hints and Help Extra Practice Module Lesson 4

6 2. A number icosahedron has 20 sides numbered 1 through 20. What is the probability that the result of a roll is a number less than 4 or greater than 11? 3. A bag contains 26 tiles, each with a different letter of the alphabet written on it. You choose a tile without looking. What is the probability that you choose a vowel (a, e, i, o, or u) or a letter in the word GEOMETRY? 4. Persevere in Problem Solving You roll two number cubes at the same time. Each cube has sides numbered 1 through 6. What is the probability that the sum of the numbers rolled is even or greater than 9? (Hint: Create and fill out a probability chart.) Cube 1 Cube 2 Module Lesson 4

7 The table shows the data for car insurance quotes for 125 drivers made by an insurance company in one week. Teen Adult (20 or over) Total 0 accidents accident accidents Total You randomly choose one of the drivers. Find the probability of each event. 5. The driver is an adult. 6. The driver is a teen with 0 or 1 accident. 7. The driver is a teen. 8. The driver has 2+ accidents. 9. The driver is a teen and has 2+ accidents. 10. The driver is a teen or a driver with 2+ accidents. Image Credits: arek_ malang/shutterstock Use the following information for Exercises The table shown shows the results of a customer satisfaction survey for a cellular service provider, by location of the customer. In the survey, customers were asked whether they would recommend a plan with the provider to a friend. Arlington Towson Parkville Total Yes No Total Module Lesson 4

8 One of the customers that was surveyed was chosen at random. Find the probability of each event. 11. The customer was from Towson and said No. 12. The customer was from Parkville. 13. The customer said Yes. 14. The customer was from Parkville and said Yes. 15. The customer was from Parkville or said Yes. 16. Explain why you cannot use the rule P (A or B) = P (A) + P (B) in Exercise 15. Use the following information for Exercises Roberto is the owner of a car dealership. He is assessing the success rate of his top three salespeople in order to offer one of them a promotion. Over two months, for each attempted sale, he records whether the salesperson made a successful sale or not. The results are shown in the chart. Successful Unsuccessful Total Becky Raul Darrell Total Roberto randomly chooses one of the attempted sales. 17. Find the probability that the sale was one of Becky s or Raul s successful sales. Module Lesson 4

9 18. Find the probability that the sale was one of the unsuccessful sales or one of Raul s successful sales. 19. Find the probability that the sale was one of Darrell s unsuccessful sales or one of Raul s unsuccessful sales. 20. Find the probability that the sale was an unsuccessful sale or one of Becky s attempted sales. 21. Find the probability that the sale was a successful sale or one of Raul s attempted sales. Module Lesson 4

10 22. You are going to draw one card at random from a standard deck of cards. A standard deck of cards has 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) in each of 4 suits (hearts, clubs, diamonds, spades). The hearts and diamonds cards are red. The clubs and spades cards are black. Which of the following have a probability of less than 1? Choose all that apply. 4 a. Drawing a card that is a spade and an ace b. Drawing a card that is a club or an ace c. Drawing a card that is a face card or a club d. Drawing a card that is black and a heart e. Drawing a red card and a number card from 2 9 H.O.T. Focus on Higher Order Thinking 23. Draw Conclusions A survey of 1108 employees at a software company finds that 621 employees take a bus to work and 445 employees take a train to work. Some employees take both a bus and a train, and 321 employees take only a train. To the nearest percent, find the probability that a randomly chosen employee takes a bus or a train to work. Explain. Image Credits: Peter Titmuss/Alamy Module Lesson 4

11 24. Communicate Mathematical Ideas Explain how to use a Venn diagram to find the probability of randomly choosing a multiple of 3 or a multiple of 4 from the set of numbers from 1 to 25. Then find the probability. A A B B S 25. Explain the Error Sanderson attempted to find the probability of randomly choosing a 10 or a diamond from a standard deck of playing cards. He used the following logic: Let S be the sample space, A be the event that the card is a 10, and B be the event that the card is a diamond. There are 52 cards in the deck, so n (S) = 52. There are four 10s in the deck, so n (A) = 4. There are 13 diamonds in the deck, so n (B) = 13. One 10 is a diamond, so n (A B) = 1. n (A B) P (A B) = _ n (A) = n (B) - n (A B) = _ = _ 51 n (S) n (S) Describe and correct Sanderson s mistake. Module Lesson 4

12 Lesson Performance Task What is the smallest number of randomly chosen people that are needed in order for there to be a better than 50% probability that at least two of them will have the same birthday? The astonishing answer is 23. Follow these steps to find why. 1. Can a person have a birthday on two different days? Use the vocabulary of this lesson to explain your answer. Looking for the probability that two or more people in a group of 23 have matching birthdays is a challenge. Maybe there is one match but maybe there are five matches or seven or fourteen. A much easier way is to look for the probability that there are no matches in a group of 23. In other words, all 23 have different birthdays. Then use that number to find the answer. 2. There are 365 days in a non-leap year. a. Write an expression for the number of ways can you assign different birthdays to 23 people. (Hint: Think of the people as standing in a line, and you are going to assign a different number from 1 to 365 to each person.) b. Write an expression for the number ways can you assign any birthday to 23 people. (Hint: Now think about assigning any number from 1 to 365 to each of 23 people.) c. How can you use your answers to (a) and (b) to find the probability that no people in a group of 23 have the same birthday? Use a calculator to find the probability to the nearest ten-thousandth. d. What is the probability that at least two people in a group of 23 have the same birthday? Explain your reasoning. Module Lesson 4

### 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

### Probability: introduction

May 6, 2009 Probability: introduction page 1 Probability: introduction Probability is the part of mathematics that deals with the chance or the likelihood that things will happen The probability of an

### 7.1 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

### 1. Theoretical probability is what should happen (based on math), while probability is what actually happens.

Name: Date: / / QUIZ DAY! Fill-in-the-Blanks: 1. Theoretical probability is what should happen (based on math), while probability is what actually happens. 2. As the number of trials increase, the experimental

### 4.3 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:

### Such 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

### 7 5 Compound Events. March 23, Alg2 7.5B Notes on Monday.notebook

7 5 Compound Events At a juice bottling factory, quality control technicians randomly select bottles and mark them pass or fail. The manager randomly selects the results of 50 tests and organizes the data

### Classical vs. Empirical Probability Activity

Name: Date: Hour : Classical vs. Empirical Probability Activity (100 Formative Points) For this activity, you will be taking part in 5 different probability experiments: Rolling dice, drawing cards, drawing

### Basic Probability. Let! = # 8 # < 13, # N -,., and / are the subsets of! such that - = multiples of four. = factors of 24 / = square numbers

Basic Probability Let! = # 8 # < 13, # N -,., and / are the subsets of! such that - = multiples of four. = factors of 24 / = square numbers (a) List the elements of!. (b) (i) Draw a Venn diagram to show

### Chapter 1: Sets and Probability

Chapter 1: Sets and Probability Section 1.3-1.5 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

### Define and Diagram Outcomes (Subsets) of the Sample Space (Universal Set)

12.3 and 12.4 Notes Geometry 1 Diagramming the Sample Space using Venn Diagrams A sample space represents all things that could occur for a given event. In set theory language this would be known as the

### Chapter 5: Probability: What are the Chances? Section 5.2 Probability Rules

+ Chapter 5: Probability: What are the Chances? Section 5.2 + Two-Way Tables and Probability When finding probabilities involving two events, a two-way table can display the sample space in a way that

### Unit 1 Day 1: Sample Spaces and Subsets. Define: Sample Space. Define: Intersection of two sets (A B) Define: Union of two sets (A B)

Unit 1 Day 1: Sample Spaces and Subsets Students will be able to (SWBAT) describe events as subsets of sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions,

### 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

### Review. Natural Numbers: Whole Numbers: Integers: Rational Numbers: Outline Sec Comparing Rational Numbers

FOUNDATIONS Outline Sec. 3-1 Gallo Name: Date: Review Natural Numbers: Whole Numbers: Integers: Rational Numbers: Comparing Rational Numbers Fractions: A way of representing a division of a whole into

### 19.3 Combinations and Probability

Name Class Date 19.3 Combinations and Probability Essential Question: What is the difference between a permutaion and a combination? Explore Finding the Number of Combinations A combination is a selection

### Name Date Class. 2. dime. 3. nickel. 6. randomly drawing 1 of the 4 S s from a bag of 100 Scrabble tiles

Name Date Class Practice A Tina has 3 quarters, 1 dime, and 6 nickels in her pocket. Find the probability of randomly drawing each of the following coins. Write your answer as a fraction, as a decimal,

### 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

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

MATH 205 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM # - SPRING 2006 - DR. DAVID BRIDGE TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Tell whether the statement is

### Intermediate Math Circles November 1, 2017 Probability I

Intermediate Math Circles November 1, 2017 Probability I 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.

### Mutually Exclusive Events

Mutually Exclusive Events Suppose you are rolling a six-sided die. What is the probability that you roll an odd number and you roll a 2? Can these both occur at the same time? Why or why not? Mutually

### Quiz 2 Review - on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II??

Quiz 2 Review - on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II?? Some things to Know, Memorize, AND Understand how to use are n What are the formulas? Pr ncr Fill in the notation

### MULTIPLE 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

### Section Introduction to Sets

Section 1.1 - Introduction to Sets Definition: A set is a well-defined collection of objects usually denoted by uppercase letters. Definition: The elements, or members, of a set are denoted by lowercase

### 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

### CHAPTER 7 Probability

CHAPTER 7 Probability 7.1. Sets A set is a well-defined collection of distinct objects. Welldefined means that we can determine whether an object is an element of a set or not. Distinct means that we can

### Algebra 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)

### 2 Event is equally likely to occur or not occur. When all outcomes are equally likely, the theoretical probability that an event A will occur is:

10.3 TEKS a.1, a.4 Define and Use Probability Before You determined the number of ways an event could occur. Now You will find the likelihood that an event will occur. Why? So you can find real-life geometric

### 4. Are events C and D independent? Verify your answer with a calculation.

Honors Math 2 More Conditional Probability Name: Date: 1. A standard deck of cards has 52 cards: 26 Red cards, 26 black cards 4 suits: Hearts (red), Diamonds (red), Clubs (black), Spades (black); 13 of

### INDEPENDENT AND DEPENDENT EVENTS UNIT 6: PROBABILITY DAY 2

INDEPENDENT AND DEPENDENT EVENTS UNIT 6: PROBABILITY DAY 2 WARM UP Students in a mathematics class pick a card from a standard deck of 52 cards, record the suit, and return the card to the deck. The results

### Section 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

### 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

### Grade 6 Math Circles Fall Oct 14/15 Probability

1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 6 Math Circles Fall 2014 - Oct 14/15 Probability Probability is the likelihood of an event occurring.

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

6. Practice Problems Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the probability. ) A bag contains red marbles, blue marbles, and 8

### Unit 11 Probability. Round 1 Round 2 Round 3 Round 4

Study Notes 11.1 Intro to Probability Unit 11 Probability Many events can t be predicted with total certainty. The best thing we can do is say how likely they are to happen, using the idea of probability.

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

MATH 205 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING 2009 - DR. DAVID BRIDGE TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Tell whether the statement is

### ATHS FC Math Department Al Ain Remedial worksheet. Lesson 10.4 (Ellipses)

ATHS FC Math Department Al Ain Remedial worksheet Section Name ID Date Lesson Marks Lesson 10.4 (Ellipses) 10.4, 10.5, 0.4, 0.5 and 0.6 Intervention Plan Page 1 of 19 Gr 12 core c 2 = a 2 b 2 Question

### Probability - 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

### (a) Suppose you flip a coin and roll a die. Are the events obtain a head and roll a 5 dependent or independent events?

Unit 6 Probability Name: Date: Hour: Multiplication Rule of Probability By the end of this lesson, you will be able to Understand Independence Use the Multiplication Rule for independent events Independent

### Mutually Exclusive Events Algebra 1

Name: Mutually Exclusive Events Algebra 1 Date: Mutually exclusive events are two events which have no outcomes in common. The probability that these two events would occur at the same time is zero. Exercise

### Independence Is The Word

Problem 1 Simulating Independent Events Describe two different events that are independent. Describe two different events that are not independent. The probability of obtaining a tail with a coin toss

### 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

### 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

### 13-6 Probabilities of Mutually Exclusive Events

Determine whether the events are mutually exclusive or not mutually exclusive. Explain your reasoning. 1. drawing a card from a standard deck and getting a jack or a club The jack of clubs is an outcome

### 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:

### PROBABILITY. Example 1 The probability of choosing a heart from a deck of cards is given by

Classical Definition of Probability PROBABILITY Probability is the measure of how likely an event is. An experiment is a situation involving chance or probability that leads to results called outcomes.

### 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

### Activity 1: Play comparison games involving fractions, decimals and/or integers.

Students will be able to: Lesson Fractions, Decimals, Percents and Integers. Play comparison games involving fractions, decimals and/or integers,. Complete percent increase and decrease problems, and.

### Outcomes: The outcomes of this experiment are yellow, blue, red and green.

(Adapted from http://www.mathgoodies.com/) 1. Sample Space The sample space of an experiment is the set of all possible outcomes of that experiment. The sum of the probabilities of the distinct outcomes

### Probability 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,

### If 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

### CC-13. Start with a plan. How many songs. are there MATHEMATICAL PRACTICES

CC- Interactive Learning Solve It! PURPOSE To determine the probability of a compound event using simple probability PROCESS Students may use simple probability by determining the number of favorable outcomes

### Lesson 17.1 Assignment

Lesson 17.1 Assignment Name Date Is It Better to Guess? Using Models for Probability Charlie got a new board game. 1. The game came with the spinner shown. 6 7 9 2 3 4 a. List the sample space for using

### Chapter 1 - Set Theory

Midterm review Math 3201 Name: Chapter 1 - Set Theory Part 1: Multiple Choice : 1) U = {hockey, basketball, golf, tennis, volleyball, soccer}. If B = {sports that use a ball}, which element would be in

### Probability Review before Quiz. Unit 6 Day 6 Probability

Probability Review before Quiz Unit 6 Day 6 Probability Warm-up: Day 6 1. A committee is to be formed consisting of 1 freshman, 1 sophomore, 2 juniors, and 2 seniors. How many ways can this committee be

### 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

### Key Concept Probability of Independent Events. Key Concept Probability of Mutually Exclusive Events. Key Concept Probability of Overlapping Events

15-4 Compound Probability TEKS FOCUS TEKS (1)(E) Apply independence in contextual problems. TEKS (1)(B) Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy,

### Grade 7/8 Math Circles February 25/26, Probability

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Probability Grade 7/8 Math Circles February 25/26, 2014 Probability Centre for Education in Mathematics and Computing Probability is the study of how likely

### Name (Place your name here and on the Scantron form.)

MATH 053 - CALCULUS & STATISTICS/BUSN - CRN 0398 - EXAM # - WEDNESDAY, FEB 09 - DR. BRIDGE Name (Place your name here and on the Scantron form.) MULTIPLE CHOICE. Choose the one alternative that best completes

### 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

### When a number cube is rolled once, the possible numbers that could show face up are

C3 Chapter 12 Understanding Probability Essential question: How can you describe the likelihood of an event? Example 1 Likelihood of an Event When a number cube is rolled once, the possible numbers that

### Name Date. Sample Spaces and Probability For use with Exploration 12.1

. Sample Spaces and Probability For use with Exploration. Essential Question How can you list the possible outcomes in the sample space of an experiment? The sample space of an experiment is the set of

### Math 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,

### Math 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,

### ABE/ASE Standards Mathematics

[Lesson Title] TEACHER NAME PROGRAM NAME Program Information Playing the Odds [Unit Title] Data Analysis and Probability NRS EFL(s) 3 4 TIME FRAME 240 minutes (double lesson) ABE/ASE Standards Mathematics

### STATISTICS and PROBABILITY GRADE 6

Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition STATISTICS and PROBABILITY GRADE 6 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may use

### Name: Probability, Part 1 March 4, 2013

1) Assuming all sections are equal in size, what is the probability of the spinner below stopping on a blue section? Write the probability as a fraction. 2) A bag contains 3 red marbles, 4 blue marbles,

### Unit 7 - Probability Review

Name: Date:. The table below shows the number of colored marbles Maury has in his collection. Color Marble Collection Number of Marbles Purple 5 Blue 4 Red 9 Green 2 If Maury picks a marble without looking,

### Probability Review Questions

Probability Review Questions Short Answer 1. State whether the following events are mutually exclusive and explain your reasoning. Selecting a prime number or selecting an even number from a set of 10

### Name: Date: Interim 1-3 ACT Aspire, Pro-Core, and AIR Practice Site Statistics and Probability Int Math 2

1. Standard: S.ID.C.7: The graph below models a constant decrease in annual licorice sales for Licorice Company, Inc., from 1998 through 2000. The points have been connected to illustrate the trend. Which

### This Probability Packet Belongs to:

This Probability Packet Belongs to: 1 2 Station #1: M & M s 1. What is the sample space of your bag of M&M s? 2. Find the theoretical probability of the M&M s in your bag. Then, place the candy back into

### FALL 2012 MATH 1324 REVIEW EXAM 4

FALL 01 MATH 134 REVIEW EXAM 4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the sample space for the given experiment. 1) An ordinary die

### SALES AND MARKETING Department MATHEMATICS. Combinatorics and probabilities. Tutorials and exercises

SALES AND MARKETING Department MATHEMATICS 2 nd Semester Combinatorics and probabilities Tutorials and exercises Online document : http://jff-dut-tc.weebly.com section DUT Maths S2 IUT de Saint-Etienne

### Algebra II Probability and Statistics

Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Slide 3 / 241 Table of Contents click on the topic to go to that section Sets Independence and Conditional Probability

### 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

### MC215: MATHEMATICAL REASONING AND DISCRETE STRUCTURES

MC215: MATHEMATICAL REASONING AND DISCRETE STRUCTURES Thursday, 4/17/14 The Addition Principle The Inclusion-Exclusion Principle The Pigeonhole Principle Reading: [J] 6.1, 6.8 [H] 3.5, 12.3 Exercises:

### Algebra II. Sets. Slide 1 / 241 Slide 2 / 241. Slide 4 / 241. Slide 3 / 241. Slide 6 / 241. Slide 5 / 241. Probability and Statistics

Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Slide 3 / 241 Slide 4 / 241 Table of Contents click on the topic to go to that section Sets Independence and Conditional

### Algebra II. Slide 1 / 241. Slide 2 / 241. Slide 3 / 241. Probability and Statistics. Table of Contents click on the topic to go to that section

Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 241 Sets Independence and Conditional Probability

### Making Predictions with Theoretical Probability. ESSENTIAL QUESTION How do you make predictions using theoretical probability?

L E S S O N 13.3 Making Predictions with Theoretical Probability 7.SP.3.6 predict the approximate relative frequency given the probability. Also 7.SP.3.7a ESSENTIAL QUESTION How do you make predictions

### Key Concepts. Theoretical Probability. Terminology. Lesson 11-1

Key Concepts Theoretical Probability Lesson - Objective Teach students the terminology used in probability theory, and how to make calculations pertaining to experiments where all outcomes are equally

### ABC High School, Kathmandu, Nepal. Topic : Probability

BC High School, athmandu, Nepal Topic : Probability Grade 0 Teacher: Shyam Prasad charya. Objective of the Module: t the end of this lesson, students will be able to define and say formula of. define Mutually

### 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

### This unit will help you work out probability and use experimental probability and frequency trees. Key points

Get started Probability This unit will help you work out probability and use experimental probability and frequency trees. AO Fluency check There are 0 marbles in a bag. 9 of the marbles are red, 7 are

### Basic Concepts of Probability and Counting Section 3.1

Basic Concepts of Probability and Counting Section 3.1 Summer 2013 - Math 1040 June 17 (1040) M 1040-3.1 June 17 1 / 12 Roadmap Basic Concepts of Probability and Counting Pages 128-137 Counting events,

### Unit 7 Central Tendency and Probability

Name: Block: 7.1 Central Tendency 7.2 Introduction to Probability 7.3 Independent Events 7.4 Dependent Events 7.1 Central Tendency A central tendency is a central or value in a data set. We will look at

### MAT104: Fundamentals of Mathematics II Counting Techniques Class Exercises Solutions

MAT104: Fundamentals of Mathematics II Counting Techniques Class Exercises Solutions 1. Appetizers: Salads: Entrées: Desserts: 2. Letters: (A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U,

### Permutations: The number of arrangements of n objects taken r at a time is. P (n, r) = n (n 1) (n r + 1) =

Section 6.6: Mixed Counting Problems We have studied a number of counting principles and techniques since the beginning of the course and when we tackle a counting problem, we may have to use one or a

### Probability. Dr. Zhang Fordham Univ.

Probability! Dr. Zhang Fordham Univ. 1 Probability: outline Introduction! Experiment, event, sample space! Probability of events! Calculate Probability! Through counting! Sum rule and general sum rule!

### 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

### 10.2 Theoretical Probability and its Complement

warm-up after 10.1 1. A traveler can choose from 3 airlines, 5 hotels and 4 rental car companies. How many arrangements of these services are possible? 2. Your school yearbook has an editor and assistant

### A. 15 B. 24 C. 45 D. 54

A spinner is divided into 8 equal sections. Lara spins the spinner 120 times. It lands on purple 30 times. How many more times does Lara need to spin the spinner and have it land on purple for the relative

### 1324 Test 1 Review Page 1 of 10

1324 Test 1 Review Page 1 of 10 Review for Exam 1 Math 1324 TTh Chapters 7, 8 Problems 1-10: Determine whether the statement is true or false. 1. {5} {4,5, 7}. 2. {4,5,7}. 3. {4,5} {4,5,7}. 4. {4,5} {4,5,7}

### Probability and Statistics 15% of EOC

MGSE9-12.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

### Mixed Counting Problems

We have studied a number of counting principles and techniques since the beginning of the course and when we tackle a counting problem, we may have to use one or a combination of these principles. The

### Chapter 3: Probability (Part 1)

Chapter 3: Probability (Part 1) 3.1: Basic Concepts of Probability and Counting Types of Probability There are at least three different types of probability Subjective Probability is found through people

### Independent and Mutually Exclusive Events

Independent and Mutually Exclusive Events By: OpenStaxCollege Independent and mutually exclusive do not mean the same thing. Independent Events Two events are independent if the following are true: P(A

### Bell Work. Warm-Up Exercises. Two six-sided dice are rolled. Find the probability of each sum or 7

Warm-Up Exercises Two six-sided dice are rolled. Find the probability of each sum. 1. 7 Bell Work 2. 5 or 7 3. You toss a coin 3 times. What is the probability of getting 3 heads? Warm-Up Notes Exercises

### Def: 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: