# Probability Review before Quiz. Unit 6 Day 6 Probability

Size: px
Start display at page:

Transcription

1 Probability Review before Quiz Unit 6 Day 6 Probability

2 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 formed from 5 freshmen, 5 sophomores, 8 juniors, and 10 seniors? 2. Consider a deck of cards labeled Let set A = even #s and set B = # greater than 8. Find the P(A or B). (Remember, this is P(A U B). ) 3. Using the situation from problem #2, what is the probability you select an even number given you selected a number greater than 8? (Remember, this is P(A B). ) 4. A gift store sells gym bags in 10 colors, with 8 straps, and 2 designs. How many different gym bags are available? 5. The ski club with ten members is to choose three officers captain, cocaptain, and secretary. How many ways can those offices be filled? 6. The local pizza shop allows you to order a pizza with at most 5 toppings for \$9.99. If there are a total of 12 types of toppings, how many different pizzas could you order? Done Early? Work on the Given with Tree Diagrams section at the end of the Notes Handout

3 Warm-up Answers 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 formed from 5 freshmen, 5 sophomores, 8 juniors, and 10 seniors? 31,500 5C1 5C1 8C2 10C2 2. Consider a set of cards labeled Let set A = even numbers and set B = # greater than 8. Find the probability of A or B. P(A or B) = 5/10 + 2/10 1/10 = 6/10 = 3/5 3. Using the situation from problem #3, what is the probability you select an even number given you selected a number greater than 8? (1/10) / (2/10) = 5/10 = 1/2

4 Warm-up Answers 4. A gift store sells gym bags in 10 colors, with 8 straps, and 2 designs. How many different gym bags are available? 10(8)(2)= The ski club with ten members is to choose three officers captain, co-captain, and secretary. How many ways can those offices be filled? 10P 3 = The local pizza shop allows you to order a pizza with at most 5 toppings for \$9.99. If there are a total of 12 types of toppings, how many different pizzas could you order? 12C C C C C C 0 = 1586

5 Homework Discussion

6 Tonight s Homework Packet p. 12 and 13 Omit problem #1 & 2 for now Please complete #1 and 2 also Study for Quiz - Tomorrow!

7 Complete #1-9 On last page of notes handout Ex: Suppose you manage a restaurant that serves chicken wings that are mild or hot, and boneless or regular. From your experience you know that of boneless wings bought, 75% of them are mild, and of the regular wings bought, 70% are hot. Only 4 out of 10 costumers buy boneless wings. 1) Create a tree diagram for the scenario displaying all the possibilities and probabilities. Mild Wings 0.40 Boneless Hot 0.40 * 0.75 = * 0.25 = Bones 0.30 Mild 0.60 * 0.30 = Hot 0.60 * 0.70 = 0.42

8 2) P(boneless and hot wings) 3) P(hot boneless) (.4)(.25) (.4) 4) P(hot) 5) P(boneless hot) 6) P( mild wings) (.4)(.25).1 (.4)(.75) (.6)(.3).48 10%.25 25% (.4)(.25) (.6)(.7).52 52% (.4)(.25) (.4)(.25) (.6)(.7) % 48% 7) If a person orders regular wings, what is the probability they choose mild? 30% 8) P(boneless mild) (.4)(.75) % (.4)(.75) (.6)(.3) 9) Of the boneless wings, what is the probability someone orders mild? 75%

9 Practice 1) When rolling a die twice, find the probability of rolling an odd number then a multiple of 2. 2) When rolling a die twice, find the probability of rolling an odd number and a multiple of 2. 3) When rolling a die once, find the probability of rolling an number greater than 3 or a multiple of 3. 4) Mike noticed that a lot of the students taking the ACT were also taking the SAT. In fact, of the 80 students in his grade, 32 students were taking the ACT, 48 students were taking the SAT, and 12 students took both the ACT and the SAT. a) Draw a Venn diagram and help Mike with his calculations. b) Calculate P(ACT U SAT) c) Calculate P(ACT SAT) d) Calculate the probability of selecting a student at random who was either taking the ACT or SAT, but not both. e) Calculate P(Not taking any test c )

10 Practice Answers 1) When rolling a die twice, find the probability of rolling an odd number then a multiple of 2. P(odd) * P(mult. of 2) = 3/6 * 3/6 = 9/36 = 1/4 2) When rolling a die twice, find the probability of rolling an odd number and a multiple of 2. P(odd, then mult. of 2) + P(mult. of 2, then odd) P(odd) * P(mult. of 2) + P(mult. of 2) * P(odd) = 3/6 * 3/6 + 3/6 * 3/6 = 9/36 + 9/36 = 1/2 3) When rolling a die once, find the probability of rolling an number greater than 3 or a multiple of 3. Mutually Inclusive Events P(>3) + P(mult. of 3) P(>3 & mult. of 3) = 3/6 + 2/6-1/6 = 4/6 = 2/3

11 Practice Answers 4) Mike noticed that a lot of the students taking the ACT were also taking the SAT. In fact, of the 80 students in his grade, 32 students were taking the ACT, 48 students were taking the SAT, and 12 students took both the ACT and the SAT. a) Draw a Venn diagram and help Jack with his calculations. Grade ACT SAT 36 b) Calculate P(ACT U SAT) = take ACT or SAT = 68/80 = 17/20 c) Calculate P(ACT SAT) = take ACT & SAT = 12/80 = 3/20 d) Calculate the probability of selecting a student at random who was either taking the ACT or SAT, but not both. 56/80 = 7/10 e) Calculate P(Not taking any test c ) = complement of not taking the test = taking a test = 68/80 = 17/20 12

12 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 Intersection of two sets (A B) : Fill in the vocab. Union of two sets (A B) : Complement of a set: P(not A) = P( ) = Factorial: For any integer n>0, n! =n(n-1)(n-2)(n-3) (3)(2)(1) If n=0, 0! = Ex: 4! = If A and B are Independent events, then P(A and B) = P(A B) = If A and B are Dependent events, then P(A, then B) = If A and B are Mutually Inclusive or Exclusive Events P(A or B) = P(A B) = If A and B are Conditional Events P(A given B) = P(A B) =

13 Quiz 2 Review KEY Are You Ready For Your Last Quiz In Honors Math 2?? Some things to Know, Memorize, AND Understand how to use are n P r n! ( n r)! n C r n! ( n r)! r! Factorial: For any integer n>0, n! =n(n-1)(n-2)(n-3) (3)(2)(1) If n=0, 0! =1 Ex: 4! = Intersection of two sets (A B) : All the elements that appear in both sets (the overlap of the two sets) Union of two sets (A B) : Everything in either set (the items in A or B alone or both) Compliment of a set: all elements in the universal set that are NOT in the initial set P(not A) = P(A C ) = 1 - P(A) If A and B are Independent events, then P(A and B) = P(A B) = P(A) P(B) If A and B are Dependent events, then P(A, then B) = P(A) P(B after A) **assume success on 1 st draw** If A and B are Mutually Inclusive or Exclusive Events P(A or B) = P(A B) = P(A) + P(B) P(A B) If A and B are Conditional Events P(A given B) = P( A B) P(A and B) PB ( )

14 Whiteboard Review You will need: - Whiteboard - Marker - Eraser - Your brain!

15 A committee is to be formed consisting of 1 freshman, 1 sophomore, 2 juniors, and 2 seniors. How many ways can this committee be formed from 5 freshmen, 5 sophomores, 8 juniors, and 10 seniors? C C C C ,500

16 A local telephone number consists of 7 digits, and the first number cannot begin with 0 or 1. How many different local telephone numbers are possible? ,000,000

17 How many distinguishable ways can the letters in CASTRO be written? 6! = 720

18 How many distinguishable ways can the letters in MISSISSIPPI be written? 11! (4!4!2!) 34,650

19 How many different 7 card hands are possible from a standard 52 card deck? 52 C 7 = 133,784,560

20 2 coins are tossed. What is the probability of getting at least one tail? HH HT TH TT 3/4 Write as a fraction.

21 Write as a fraction. 4 coins are tossed. What is the probability of getting at least 3 tails? 5/16

22 From a standard deck of 52 cards, find the probability of getting a club, or a face card Write as a fraction.

23 John moves to Thailand, and only speaks English. On his first day of school he is given a 10 question multiple choice quiz in Thai, each with 4 options. What is the probability that John will guess all 10 questions correctly? (1/4) 10 = 9.5 x 10-7

24 A bag contains 3 blue, 4 purple, and 5 red marbles. 3 marbles are drawn. Find the probability of drawing: a) 2 red and a blue b) a blue, given you drew 2 reds a) 3/22 b) 3/10 Possibilities: red, red, blue (1/22) blue, red, red (1/22) red, blue, red (1/22) Write as a fraction.

25 A dice is rolled. Find the probability of rolling a number that is less than 5, or even Write as a fraction.

26 A store sells T-shirts in 5 colors, 9 designs, and 3 sizes. How many different T-shirts are available? 5 x 9 x 3 = 135

27 The odds of an event occurring are 15 to 7. What is the probability of the event occurring? 15/22 Write as a fraction.

28 A high school basketball team leads at halftime in 45% of the games in a season. The team wins 75% of the time when they have a halftime lead, but wins only 9% of the time when they do not have a halftime lead. Write as a percent. Round to the nearest tenth. a) What is the probability that the team wins a particular game during the season? 38.7% b) P(lose) 61.3% c) P(Does not lead win) 12.8% d) P(Leads lose) 18.4% e) Does not lead and wins 4.95%

29 Of 100 students, 23 are taking Calculus, 29 are taking French, and 12 are taking both Calculus and French. If a student is picked at random, what is the probability that the student is taking Calculus or French? 40/100= 2/5

30 In a student body election, there are three candidates for president, four candidates for vice president, and five candidates for secretary. How many possible groups of officers are there? 3 x 4 x 5 = 60 OR C C C

31 Extra Practice (if not completed)

32 Given the following Venn Diagram, how many students are taking an art AND a music class?

33

34 Given the following Venn Diagram, how many students are taking an art OR a music class?

35

36 Given the following Venn Diagram, how many students are in the Venn Diagram?

37

38 Given the following Venn Diagram, find the PROBABILITY that a student is taking an art AND a music class. P(art AND music) =

39 6 / 140 or 3 / 70

40 Given the following Venn Diagram, find the PROBABILITY that a student is taking an art OR a music class. P(art OR music) =

41 38 / 140 or 19 / 70

42 The probability of an event + the probability of its complement = P(A) + P(A C ) =

43

44 The probability of rain tomorrow is 40%. What is the probability that it doesn t rain?

45

46 The probability of rain tomorrow is 40%. What are the odds of rain?

47 4:6 or 2:3

48 At SWGHS, 30% of the students are sophomores. 48% of the students are female. What is the probability that a student is a female AND a sophomore?

49 14.4%

50 A coin and a die are tossed/rolled. What is the probability of getting tails and a 4.

51 1/12

52 If the probability of receiving a piece of mail is 25% on any given day, what is the probability of receiving a piece of mail today and no mail tomorrow?

53 18.75%

54 Given a standard deck of cards, what is the probability of drawing a diamond?

55 25%

56 Given a standard deck of cards, what is the probability of drawing a king?

57 1/13

58 Given a standard deck of cards, what is the probability of drawing the king of diamonds?

59 1/52

60 Given a standard deck of cards, what is the probability of drawing a king OR a diamond?

61 16/52 or 4/13

62 Given a standard deck of cards, what are the ODDS of drawing a diamond?

63 13:39 or 1:3

64 Tonight s Homework Packet p. 12 and 13 Omit problem #1 & 2 for now Please complete #1 and 2 also Study for Quiz - Tomorrow!

### 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

### 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

### 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

### 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

### 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:

### 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,

### 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

### 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

### 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:

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Probability of Independent and Dependent Events. CCM2 Unit 6: Probability

Probability of Independent and Dependent Events CCM2 Unit 6: Probability Independent and Dependent Events Independent Events: two events are said to be independent when one event has no affect on the 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:

### 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

### 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 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

### 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

### 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

### 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)

### 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

### 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 Unit 6 Day 3

Probability Unit 6 Day 3 Warm-up: 1. If you have a standard deck of cards in how many different hands exists of: (Show work by hand but no need to write out the full factorial!) a) 5 cards b) 2 cards 2.

### 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

### 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

### 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

### Math 7 Notes - Unit 11 Probability

Math 7 Notes - Unit 11 Probability Probability Syllabus Objective: (7.2)The student will determine the theoretical probability of an event. Syllabus Objective: (7.4)The student will compare theoretical

### 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

### NOTES Unit 6 Probability Honors Math 2 1

NOTES Unit 6 Probability Honors Math 2 1 Warm-Up: Day 1: Counting Methods, Permutations & Combinations 1. Given the equation y 4 x 2draw the graph, being sure to indicate at least 3 points clearly. Solve

### SECONDARY 2 Honors ~ Lesson 9.2 Worksheet Intro to Probability

SECONDARY 2 Honors ~ Lesson 9.2 Worksheet Intro to Probability Name Period Write all probabilities as fractions in reduced form! Use the given information to complete problems 1-3. Five students have the

### 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

### 2. The figure shows the face of a spinner. The numbers are all equally likely to occur.

MYP IB Review 9 Probability Name: Date: 1. For a carnival game, a jar contains 20 blue marbles and 80 red marbles. 1. Children take turns randomly selecting a marble from the jar. If a blue marble is chosen,

### 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

### 6) A) both; happy B) neither; not happy C) one; happy D) one; not happy

MATH 00 -- PRACTICE TEST 2 Millersville University, Spring 202 Ron Umble, Instr. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all natural

### 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

### 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

### Probability of Independent Events. If A and B are independent events, then the probability that both A and B occur is: P(A and B) 5 P(A) p P(B)

10.5 a.1, a.5 TEKS Find Probabilities of Independent and Dependent Events Before You found probabilities of compound events. Now You will examine independent and dependent events. Why? So you can formulate

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Unit 14 Probability. Target 3 Calculate the probability of independent and dependent events (compound) AND/THEN statements

Target 1 Calculate the probability of an event Unit 14 Probability Target 2 Calculate a sample space 14.2a Tree Diagrams, Factorials, and Permutations 14.2b Combinations Target 3 Calculate the probability

### 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

### 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

### 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

### 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

### Answer each of the following problems. Make sure to show your work.

Answer each of the following problems. Make sure to show your work. 1. A board game requires each player to roll a die. The player with the highest number wins. If a player wants to calculate his or her

### 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

### 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

### 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

### 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

### 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.

### 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

### 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,

### Name: Class: Date: ID: A

Class: Date: Chapter 0 review. A lunch menu consists of different kinds of sandwiches, different kinds of soup, and 6 different drinks. How many choices are there for ordering a sandwich, a bowl of soup,

### 5.5 Conditional Probability

5.5 Conditional Probability YOU WILL NEED calculator EXPLORE Jackie plays on a volleyball team called the Giants. The Giants are in a round-robin tournament with five other teams. The teams that they will

### 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

### 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

### 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

### 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

### The Teachers Circle Mar. 20, 2012 HOW TO GAMBLE IF YOU MUST (I ll bet you \$5 that if you give me \$10, I ll give you \$20.)

The Teachers Circle Mar. 2, 22 HOW TO GAMBLE IF YOU MUST (I ll bet you \$ that if you give me \$, I ll give you \$2.) Instructor: Paul Zeitz (zeitzp@usfca.edu) Basic Laws and Definitions of Probability If

### 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

### 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

### 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

### , x {1, 2, k}, where k > 0. (a) Write down P(X = 2). (1) (b) Show that k = 3. (4) Find E(X). (2) (Total 7 marks)

1. The probability distribution of a discrete random variable X is given by 2 x P(X = x) = 14, x {1, 2, k}, where k > 0. Write down P(X = 2). (1) Show that k = 3. Find E(X). (Total 7 marks) 2. In a game

### [Independent Probability, Conditional Probability, Tree Diagrams]

Name: Year 1 Review 11-9 Topic: Probability Day 2 Use your formula booklet! Page 5 Lesson 11-8: Probability Day 1 [Independent Probability, Conditional Probability, Tree Diagrams] Read and Highlight Station

### Probability Warm-Up 2

Probability Warm-Up 2 Directions Solve to the best of your ability. (1) Write out the sample space (all possible outcomes) for the following situation: A dice is rolled and then a color is chosen, blue

### 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.

### 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

### 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!

### Lecture 6 Probability

Lecture 6 Probability Example: When you toss a coin, there are only two possible outcomes, heads and tails. What if we toss a coin two times? Figure below shows the results of tossing a coin 5000 times

### 10.1 Applying the Counting Principle and Permutations (helps you count up the number of possibilities!)

10.1 Applying the Counting Principle and Permutations (helps you count up the number of possibilities!) Example 1: Pizza You are buying a pizza. You have a choice of 3 crusts, 4 cheeses, 5 meat toppings,

### 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

### 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.

### Instructions: Choose the best answer and shade the corresponding space on the answer sheet provide. Be sure to include your name and student numbers.

Math 3201 Unit 3 Probability Assignment 1 Unit Assignment Name: Part 1 Selected Response: Instructions: Choose the best answer and shade the corresponding space on the answer sheet provide. Be sure to

### 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

### 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

### 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

### 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

### Math 3201 Unit 3: Probability Name:

Multiple Choice Math 3201 Unit 3: Probability Name: 1. Given the following probabilities, which event is most likely to occur? A. P(A) = 0.2 B. P(B) = C. P(C) = 0.3 D. P(D) = 2. Three events, A, B, and

### 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

### Chapter 6: Probability and Simulation. The study of randomness

Chapter 6: Probability and Simulation The study of randomness 6.1 Randomness Probability describes the pattern of chance outcomes. Probability is the basis of inference Meaning, the pattern of chance outcomes

### 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:

### 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.

### 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

### 5.6. Independent Events. INVESTIGATE the Math. Reflecting

5.6 Independent Events YOU WILL NEED calculator EXPLORE The Fortin family has two children. Cam determines the probability that the family has two girls. Rushanna determines the probability that the family

### C) 1 4. Find the indicated probability. 2) A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

Chapter Probability Practice STA03, Broward College Answer the question. ) On a multiple choice test with four possible answers (like this question), what is the probability of answering a question correctly

### ECON 214 Elements of Statistics for Economists

ECON 214 Elements of Statistics for Economists Session 4 Probability Lecturer: Dr. Bernardin Senadza, Dept. of Economics Contact Information: bsenadza@ug.edu.gh College of Education School of Continuing

### Lenarz Math 102 Practice Exam # 3 Name: 1. A 10-sided die is rolled 100 times with the following results:

Lenarz Math 102 Practice Exam # 3 Name: 1. A 10-sided die is rolled 100 times with the following results: Outcome Frequency 1 8 2 8 3 12 4 7 5 15 8 7 8 8 13 9 9 10 12 (a) What is the experimental probability

### , -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,