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

Size: px
Start display at page:

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

Transcription

1 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 Universal Set all elements defined by that set. We often use Venn diagrams to display the relationships within sets and sample spaces. Diagramming the Universal Set (Sample Space) The universal set is usually diagrammed as a rectangle. The set name which is being used as the universal set is usually placed in the upper left hand corner of the shape. Depending on the size of the set you do not have to include all elements of the set in the diagram, usually a few are provided to give an image of some of the values of the set. If the set is small, then all elements should be listed. To diagram our sample space, the set M, a bag of marbles with 4 red marbles (solid) and 6 white marbles (empty) we create the rectangle, label it the universal set M, and then list out the elements of the set. In this case because there are only 10 elements it is easy to list them all out in the diagram. Define and Diagram Outcomes (Subsets) of the Sample Space (Universal Set) As stated earlier, a probability has two components, the sample space, which represents all possible things that could happen, and the defined successful outcomes, which represents the number of times a particular event occurs in that sample space. The outcome could be picking a heart from a deck of cards, rolling an even number on a dice, spinning a spinner and getting blue.. an outcome is simply a subset of the universal set. A subset is a collection of elements that all exist within another set. If all elements of set X belong to set Y, then it is said that set X is a subset of set Y. Any set formed with elements of the universal set is a subset of that universal set. For example if the sample space was rolling a D12 (a 12 sided dice) some subsets might be: Rolling a prime number, Set P = {2, 3, 5, 7, 11} is a subset of Rolling an even number less than 5, Set E = {2, 4} is a subset of Rolling a number greater than 12, Set B = {} is a subset of In the third example, Set B is an EMPTY SET or NULL SET. This means that no elements fit that description. The empty set gets its own special symbol, Ø. When notating an empty set we would write Set B = Ø, and NOT Set B = {Ø}. The latter notation is wrong because that set contains one element, the empty set. Thus set B would not be empty if it has one element, even if that element represents a set that has nothing. When writing that one set is a subset of another we use two special mathematical symbols, either or. The first symbol,, allows the subset to be the same as or smaller, whereas the second symbol,, forces the subset to contain less elements than the original set and these subsets are called proper subsets. Now if we look back to examples #1, #2 and #3, we would write those relationships as: Ex. #1 Set P Set U Ex. #2 Set E Set U Ex. #3 Set B Set U or Set U or Set P Set U or Set E Set U or Set B Set U or Set U

2 12.3 and 12.4 Notes Geometry 2 Diagramming a Outcome (Subset) using a Venn Diagram When a subset is defined, the elements are organized and a new boundary is drawn in the Venn diagram. So if we defined the set R as the set of all red marbles in the bag we would draw a new boundary that would contain all of those elements. Set R = {3R, 4R, 5R, 8R} Set U = {3R, 4R, 5R, 8R, 1W, 2W, 4W, 5W, 8W, 9W} Set R Set U This can easily be turned into a probability - What is the probability of picking a red marble from this bag of marbles? nr ( ) 4 P(Set R) = P(Red) = or 0.4 or 40% If we defined set E to be the set of all even numbers in the bag we could determine the probability to be: Set E = {4R, 8R, 2W, 4W, 8W} Set E Set U ne ( ) 5 P(Set E) = P(Evens) = or 0.5 or 50% Again if we defined set L to be the set of all numbers greater than 3 in the bag, we could determine the probability to be: Set L = {4R, 5R, 8R, 4W, 5W, 8W, 9W} Set L Set U nl ( ) 7 P(Set L) = P(Numbers >3) = or 0.7 or 70% The Complement of an Event, not The complement of an event is the probability of everything but that event occurring. So if the event was set A, then the complement is denoted as, set A c, everything that A is not. If the probability of picking a yellow marble from a bag is 3 8, then its complement, the probability of not yellow is. An easy way to calculate the complement is P(A c ) = 1 P(A). This works because all probabilities sum to 1 and so whatever the probability of event A happening is, the probability of it not happening is everything else or in other words, 1 P(A). This relationship is easily viewed in a Venn diagram. P(A) + P(A c ) = 1

3 12.3 and 12.4 Notes Geometry 3 When determining the probability of a complement it is usually simplest to calculate the probability of the event and then subtract it from 1. Ex. #1 Given a bag of marbles with 3 green, 2 yellow and 5 red. What is the probability of NOT getting a green marble? P(G) = P(G) = P(G c ) = 7 10 Ex. #2 When rolling a single die, what is the probability of NOT getting a 6? P(A) = P(A) = P(A c ) = 5 6 Ex. #3 When picking a card from a standard deck, what is the probability of NOT getting a diamond? 1 P(A) = P(A c ) = Mutually Exclusive or Disjoint Sets More than one subset can be defined at a time from a universal set, so for example we could define the set of all red marbles, or the set of all even numbers, or the set of red marbles with numbers greater than 3 - the list seems like it could go on forever. Sometimes when we define more than one set at a time they have no elements in common. This is known as being mutually exclusive or disjoint. Two events are mutually exclusive events if the events cannot both occur in the same trial of an experiment, for example the flip of a coin cannot be both heads and tails and thus those two events are mutually exclusive. Diagramming Disjoint Sets If we define the set R to be all red marbles and the set W to be all white marbles we get two mutually exclusive sets because they have no elements in common with each other. We diagram this relationship by drawing boundaries around each set so that they do not touch or overlap in anyway. Set R = {3R, 4R, 5R, 8R} and Set W = {1W, 2W, 4W, 5W, 8W, 9W} Another example of disjoint sets would be set E, all of the even marbles, and set O, all of the odd marbles. Set E = {4R, 8R, 2W, 4W, 8W} and Set O = {3R, 5R, 1W, 5W, 9W} In both of these cases you cannot be both red and white or even and odd, thus they are mutually exclusive.

4 12.3 and 12.4 Notes Geometry 4 The Intersection, AND Of course when we define more than one subset the sets are not always mutually exclusive. Sometimes the two sets have shared or common elements in them. The shared items or elements are called the intersection of the sets. This should make sense to a Geometry or Algebra I student because we have already discussed the intersection of two lines. The intersection of two lines is a point, the only thing they HAVE IN COMMON. The Intersection The intersection is the collection of elements that are COMMON between the sets. The symbol notation for intersection is. In general, for any two sets S and T, the set consisting of the elements belonging to BOTH set S and set T is called the intersection of sets S and T, denoted by Set S Set T. This is sometimes also described as the elements that are in set S AND in set T. An example of two sets that would have an intersection could be found easily in a standard deck of cards, the set R, all red cards, and the set Q, the set of all queens. These two sets are NOT mutually exclusive because these sets would share two elements, the queen of hearts and the queen of diamonds. These two cards are the intersection because they are in set R AND in set Q. Another example of an intersection in a deck of cards would be the set D, the diamonds, and the set F, the face cards. The cards that are in set D AND set F (the intersection) are the jack, queen, and king of diamonds. Diagramming the Intersection If we define the set R to be all red marbles and the set E to be all even numbered marbles we get two sets that have an intersection. When these two set get diagrammed they have an overlapping region, a region that represents the values that are in both sets. We usually shade that region. Set R = {3R, 4R, 5R, 8R} and Set E = {4R, 8R, 2W, 4W, 8W} Set R Set E (Set R AND Set E) = {4R, 8R} Another example of an intersection would be the set D, all numbers divisible by 3, and the set W, all the white marbles. Set D = {3R, 9W} and Set W = {1W, 2W, 4W, 5W, 8W, 9W} Set D Set W (Set D AND Set W) = {9W} Could the intersection of two sets be empty? Of course if the two sets are mutually exclusive then there will be no elements in the intersection of the two sets. For example, the set E, the even numbered marbles and set O, the odd numbered marbles, will have no elements in common and so the intersection is the empty set. Set E = {4R, 8R, 2W, 4W, 8W} and Set O = {3R, 5R, 1W, 5W, 9W} Set E Set O (Set E AND Set O) =

5 12.3 and 12.4 Notes Geometry 5 The Union, OR The union of sets is exactly what it sounds to be, the process of combining sets together to form a larger set. The union of sets is the collection of all elements from both sets. The symbol for union is (this is easier to remember nion). In general, for any two sets S and T, the set consisting of all the elements belonging to at least one of the sets S and T is called the union of S and T, denoted Set S Set T. This is sometimes also described as the elements that are in set S OR in set T. An example of a union could be found easily in a standard deck of cards, the set R, all red cards, and the set S, the set of all spades. The union of these two sets would include all the hearts, all the diamonds and all the spades. These cards are the union because it contains set R OR set S. Diagramming the Union Usually we don t change the boundaries of the original sets to represent the new union; usually we simply shade in the sets that have formed the new union. The example to the right demonstrates the union of two mutually exclusive sets, set W, the white marbles {1W, 2W, 4W, 5W, 8W, 9W} and set E, the even red marbles {4R, 8R}. Set W Set E (Set W OR Set E) {1W, 2W, 4W, 5W, 8W, 9W} {4R, 8R} = {1W, 2W, 4W, 5W, 8W, 9W, 4R, 8R} An example of a union when the two sets that would have an intersection would be the Set E, the even numbers {2W, 4W, 8W, 4R, 8R} and the set R, the red marbles {3R, 4R, 5R, 8R}. Set E Set R (Set E OR Set R) {2W, 4W, 8W, 4R, 8R} {3R, 4R, 5R, 8R} = {2W, 4W, 8W, 3R, 4R, 5R, 8R} Let me do another example, the set B, the marbles greater than 2 and the set T, the marbles with a 3 or 4. Set B Set T (Set B OR Set T) {3R, 4R, 5R, 8R, 4W, 5W, 8W, 9W} {5R, 8R, 5W, 8W, 9W} = {3R, 4R, 5R, 8R, 4W, 5W, 8W, 9W} You do not double list elements in the set. You do not double list elements in the set.

### 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

### 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

### 8.2 Union, Intersection, and Complement of Events; Odds

8.2 Union, Intersection, and Complement of Events; Odds Since we defined an event as a subset of a sample space it is natural to consider set operations like union, intersection or complement in the context

### 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. Ms. Weinstein Probability & Statistics

Probability Ms. Weinstein Probability & Statistics Definitions Sample Space The sample space, S, of a random phenomenon is the set of all possible outcomes. Event An event is a set of outcomes of a random

### 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

### Georgia Department of Education Georgia Standards of Excellence Framework GSE Geometry Unit 6

How Odd? Standards Addressed in this Task MGSE9-12.S.CP.1 Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not). MGSE9-12.S.CP.7

### 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

### 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

### 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

### 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

### Chapter 1. Probability

Chapter 1. Probability 1.1 Basic Concepts Scientific method a. For a given problem, we define measures that explains the problem well. b. Data is collected with observation and the measures are calculated.

### 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

### 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.

### 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:

### Chapter 1. Probability

Chapter 1. Probability 1.1 Basic Concepts Scientific method a. For a given problem, we define measures that explains the problem well. b. Data is collected with observation and the measures are calculated.

### Section 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.

### Probability and Randomness. Day 1

Probability and Randomness Day 1 Randomness and Probability The mathematics of chance is called. The probability of any outcome of a chance process is a number between that describes the proportion of

### 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

### 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,

### 10-4 Theoretical Probability

Problem of the Day A spinner is divided into 4 different colored sections. It is designed so that the probability of spinning red is twice the probability of spinning green, the probability of spinning

### 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!

### 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

### 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

### 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

### 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

### 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.

### 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:

### 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,

### Probability Models. Section 6.2

Probability Models Section 6.2 The Language of Probability What is random? Empirical means that it is based on observation rather than theorizing. Probability describes what happens in MANY trials. Example

### Sample Spaces, Events, Probability

Sample Spaces, Events, Probability CS 3130/ECE 3530: Probability and Statistics for Engineers August 28, 2014 Sets A set is a collection of unique objects. Sets A set is a collection of unique objects.

### 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

### 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

### In how many ways can the letters of SEA be arranged? In how many ways can the letters of SEE be arranged?

-Pick up Quiz Review Handout by door -Turn to Packet p. 5-6 In how many ways can the letters of SEA be arranged? In how many ways can the letters of SEE be arranged? - Take Out Yesterday s Notes we ll

### 4.2.4 What if both events happen?

4.2.4 What if both events happen? Unions, Intersections, and Complements In the mid 1600 s, a French nobleman, the Chevalier de Mere, was wondering why he was losing money on a bet that he thought was

### Day 5: Mutually Exclusive and Inclusive Events. Honors Math 2 Unit 6: Probability

Day 5: Mutually Exclusive and Inclusive Events Honors Math 2 Unit 6: Probability Warm-up on Notebook paper (NOT in notes) 1. A local restaurant is offering taco specials. You can choose 1, 2 or 3 tacos

### Applications of Probability

Applications of Probability CK-12 Kaitlyn Spong Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive

### Probability is often written as a simplified fraction, but it can also be written as a decimal or percent.

CHAPTER 1: PROBABILITY 1. Introduction to Probability L EARNING TARGET: I CAN DETERMINE THE PROBABILITY OF AN EVENT. What s the probability of flipping heads on a coin? Theoretically, it is 1/2 1 way to

### Chapter 1. Set Theory

Chapter 1 Set Theory 1 Section 1.1: Types of Sets and Set Notation Set: A collection or group of distinguishable objects. Ex. set of books, the letters of the alphabet, the set of whole numbers. You can

### Probability. The MEnTe Program Math Enrichment through Technology. Title V East Los Angeles College

Probability The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College 2003 East Los Angeles College. All rights reserved. Topics Introduction Empirical Probability Theoretical

### Block 1 - Sets and Basic Combinatorics. Main Topics in Block 1:

Block 1 - Sets and Basic Combinatorics Main Topics in Block 1: A short revision of some set theory Sets and subsets. Venn diagrams to represent sets. Describing sets using rules of inclusion. Set operations.

### "Well, statistically speaking, you are for more likely to have an accident at an intersection, so I just make sure that I spend less time there.

6.2 Probability Models There was a statistician who, when driving his car, would always accelerate hard before coming to an intersection, whiz straight through it, and slow down again once he was beyond

### Section 7.3 and 7.4 Probability of Independent Events

Section 7.3 and 7.4 Probability of Independent Events Grade 7 Review Two or more events are independent when one event does not affect the outcome of the other event(s). For example, flipping a coin and

### 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

### 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

### Probability MAT230. Fall Discrete Mathematics. MAT230 (Discrete Math) Probability Fall / 37

Probability MAT230 Discrete Mathematics Fall 2018 MAT230 (Discrete Math) Probability Fall 2018 1 / 37 Outline 1 Discrete Probability 2 Sum and Product Rules for Probability 3 Expected Value MAT230 (Discrete

### 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

### 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

### Probability. Probabilty Impossibe Unlikely Equally Likely Likely Certain

PROBABILITY Probability The likelihood or chance of an event occurring If an event is IMPOSSIBLE its probability is ZERO If an event is CERTAIN its probability is ONE So all probabilities lie between 0

### CHAPTERS 14 & 15 PROBABILITY STAT 203

CHAPTERS 14 & 15 PROBABILITY STAT 203 Where this fits in 2 Up to now, we ve mostly discussed how to handle data (descriptive statistics) and how to collect data. Regression has been the only form of statistical

### Lesson Lesson 3.7 ~ Theoretical Probability

Theoretical Probability Lesson.7 EXPLORE! sum of two number cubes Step : Copy and complete the chart below. It shows the possible outcomes of one number cube across the top, and a second down the left

### 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

### The probability set-up

CHAPTER 2 The probability set-up 2.1. Introduction and basic theory We will have a sample space, denoted S (sometimes Ω) that consists of all possible outcomes. For example, if we roll two dice, the sample

### 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.

### 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,

### 4.3 Finding Probability Using Sets

4.3 Finding Probability Using ets When rolling a die with sides numbered from 1 to 20, if event A is the event that a number divisible by 5 is rolled: a) What is the sample space,? b) What is the event

### Textbook: pp Chapter 2: Probability Concepts and Applications

1 Textbook: pp. 39-80 Chapter 2: Probability Concepts and Applications 2 Learning Objectives After completing this chapter, students will be able to: Understand the basic foundations of probability analysis.

### 19.4 Mutually Exclusive and Overlapping Events

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

### 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

### 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

### 1MA01: Probability. Sinéad Ryan. November 12, 2013 TCD

1MA01: Probability Sinéad Ryan TCD November 12, 2013 Definitions and Notation EVENT: a set possible outcomes of an experiment. Eg flipping a coin is the experiment, landing on heads is the event If an

### (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

### Probability Simulation User s Manual

Probability Simulation User s Manual Documentation of features and usage for Probability Simulation Copyright 2000 Corey Taylor and Rusty Wagner 1 Table of Contents 1. General Setup 3 2. Coin Section 4

### November 6, Chapter 8: Probability: The Mathematics of Chance

Chapter 8: Probability: The Mathematics of Chance November 6, 2013 Last Time Crystallographic notation Groups Crystallographic notation The first symbol is always a p, which indicates that the pattern

### 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.

### Probability (Devore Chapter Two)

Probability (Devore Chapter Two) 1016-351-01 Probability Winter 2011-2012 Contents 1 Axiomatic Probability 2 1.1 Outcomes and Events............................... 2 1.2 Rules of Probability................................

### 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

### Probability - Grade 10 *

OpenStax-CNX module: m32623 1 Probability - Grade 10 * Rory Adams Free High School Science Texts Project Sarah Blyth Heather Williams This work is produced by OpenStax-CNX and licensed under the Creative

### Compound Probability. A to determine the likelihood of two events occurring at the. ***Events can be classified as independent or dependent events.

Probability 68B A to determine the likelihood of two events occurring at the. ***Events can be classified as independent or dependent events. Independent Events are events in which the result of event

### Probability CK-12. Say Thanks to the Authors Click (No sign in required)

Probability CK-12 Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit www.ck12.org

### NC MATH 2 NCFE FINAL EXAM REVIEW Unit 6 Probability

NC MATH 2 NCFE FINAL EXAM REVIEW Unit 6 Probability Theoretical Probability A tube of sweets contains 20 red candies, 8 blue candies, 8 green candies and 4 orange candies. If a sweet is taken at random

### CSC/MATA67 Tutorial, Week 12

CSC/MATA67 Tutorial, Week 12 November 23, 2017 1 More counting problems A class consists of 15 students of whom 5 are prefects. Q: How many committees of 8 can be formed if each consists of a) exactly

### Compound Probability. Set Theory. Basic Definitions

Compound Probability Set Theory A probability measure P is a function that maps subsets of the state space Ω to numbers in the interval [0, 1]. In order to study these functions, we need to know some basic

### Chapter 4: Probability and Counting Rules

Chapter 4: Probability and Counting Rules Before we can move from descriptive statistics to inferential statistics, we need to have some understanding of probability: Ch4: Probability and Counting Rules

### 5 Elementary Probability Theory

5 Elementary Probability Theory 5.1 What is Probability? The Basics We begin by defining some terms. Random Experiment: any activity with a random (unpredictable) result that can be measured. Trial: one

### Simple Probability. Arthur White. 28th September 2016

Simple Probability Arthur White 28th September 2016 Probabilities are a mathematical way to describe an uncertain outcome. For eample, suppose a physicist disintegrates 10,000 atoms of an element A, and

### The probability set-up

CHAPTER The probability set-up.1. Introduction and basic theory We will have a sample space, denoted S sometimes Ω that consists of all possible outcomes. For example, if we roll two dice, the sample space

### Probability: Terminology and Examples Spring January 1, / 22

Probability: Terminology and Examples 18.05 Spring 2014 January 1, 2017 1 / 22 Board Question Deck of 52 cards 13 ranks: 2, 3,..., 9, 10, J, Q, K, A 4 suits:,,,, Poker hands Consists of 5 cards A one-pair

### Venn Diagram Problems

Venn Diagram Problems 1. In a mums & toddlers group, 15 mums have a daughter, 12 mums have a son. a) Julia says 15 + 12 = 27 so there must be 27 mums altogether. Explain why she could be wrong: b) There

### I. WHAT IS PROBABILITY?

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

### Topic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes

Worksheet 6 th Topic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of

### 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

### Name: Exam 1. September 14, 2017

Department of Mathematics University of Notre Dame Math 10120 Finite Math Fall 2017 Name: Instructors: Basit & Migliore Exam 1 September 14, 2017 This exam is in two parts on 9 pages and contains 14 problems

### Chapter 5 - Elementary Probability Theory

Chapter 5 - Elementary Probability Theory Historical Background Much of the early work in probability concerned games and gambling. One of the first to apply probability to matters other than gambling

### 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

### 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

### 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

### Worksheets for GCSE Mathematics. Probability. mr-mathematics.com Maths Resources for Teachers. Handling Data

Worksheets for GCSE Mathematics Probability mr-mathematics.com Maths Resources for Teachers Handling Data Probability Worksheets Contents Differentiated Independent Learning Worksheets Probability Scales

### Objective: Determine empirical probability based on specific sample data. (AA21)

Do Now: What is an experiment? List some experiments. What types of things does one take a "chance" on? Mar 1 3:33 PM Date: Probability - Empirical - By Experiment Objective: Determine empirical probability

### Name Date. Goal: Understand sets and set notation.

F Math 12 3.1 Types of Sets and Set Notation p. 146 Name Date Goal: Understand sets and set notation. 1. set: A collection of distinguishable objects; for example, the set of whole numbers is W = {0, 1,

### More Probability: Poker Hands and some issues in Counting

More Probability: Poker Hands and some issues in Counting Data From Thursday Everybody flipped a pair of coins and recorded how many times they got two heads, two tails, or one of each. We saw that the

### Lesson 3: Chance Experiments with Equally Likely Outcomes

Lesson : Chance Experiments with Equally Likely Outcomes Classwork Example 1 Jamal, a 7 th grader, wants to design a game that involves tossing paper cups. Jamal tosses a paper cup five times and records

### 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

### 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

### 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

### 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