# 4.1 What is Probability?

Size: px
Start display at page:

Transcription

1 4.1 What is Probability? between 0 and 1 to indicate the likelihood of an event. We use event is to occur. 1

2 use three major methods: 1) Intuition 3) Equally Likely Outcomes Intuition - prediction based on previous outcomes. Relative Frequency - we have already discussed what relative frequency is when we looked at Probability Formula for Relative Frequency Probability of an Event = f n Wherefis the frequency of an event, andnis the sample size. Example: What is the probability of selecting a female student in this class? In the long run, as the sample size increases and increases, the relative frequency of outcomes get closer and closer to the theoretical (or actual) probability value. An example of how the law of large numbers works is gambling at a casino. Equally Likely Outcomes - when events have the same chance of happening. Example: The probability of correctly guessing the answer to true-false questions. Probability of an Event = number of outcomes favorable to an event total number of outcomes Can you think of any other situations where there are equally likely outcomes? 2

3 Sample Space results in a definite outcome. Usually the outcome is in the form of a description, count, or measurement. For example: If you toss a coin, there are only 2 possible outcomes (heads or tails). Sample Space- set of all possible outcomes. It is especially convenient to know the sample space where all outcomes are likely because then we can compute probabilities of various events using the following formula. total number of outcomes 3

4 4

5 Five Important Facts about Probability probability is, the more likely the event is. 3) The sum of the probabilities of outcomes in a sample space is 1. 4) Probabilities can be assigned by using three methods: intuition, relative or the formula for equally likely outcomes. 5) The probability that an event occurs plus the probability that the same event does not occur is 1. 5

6 Examples 1) If the probability that an event will occur is p, what is the probability that the event will not occur? a) p c) p - 1 d) 1 - p 2) If the probability that an event will occur is x/4, what is the probability that the event will not occur? a) (1 - x)/4 c) (4 - x)/x d) (4 - x)/4 3) If two fair dice are tossed once, the probability of getting 12 is 1/36. What is the probability of not getting 12? a) 35/36 b) 6/36 c) 30/36 d) 34/36 4) On a test the probability of getting the correct answer to a certain question is represented by x/7. Which of the following can not be a value of x? a) -1 c) 7 5) When a number is chosen at random from the set {1,2,3,4,5,6}, which one of the following events has the greatest probability of occurring? a) not choosing either 1 or 6 c) choosing a number greater than 3 b) choosing an even number d) choosing a prime number 6) The probability of drawing a red marble from a sack of marbles is 2/5. Which one of the following sets of marbles could the sack contain? a) 4 red marbles and 6 green marbles c) 2 red marbles and 5 green marbles b) 6 red marbles and 15 green marbles d) 2 red marbles, 1 blue marble, 4 white marbles probability that it is not green? b) 1/9 c) 5/9 d) 4/9 probability that it is not green? a) 3/5 b) 2/5 c) 4/5 d) 1/5 9) The footlights of a stage have 12 red bulbs, 8 blue bulbs, and 10 yellow bulbs. If all the bulbs are expected to last the same amount of time, what is the probability that a yellow bulb will burn out first? a) 20/30 b) 10/20 c) 10/30 d) 1/30 10) During a half hour of television programming, eight minutes is used for commercials. If a television set is turned on at a random time during the half hour, what is the probability that a commercial is not being shown? b) 1 c) 22/30 d) 0 6

7 4.2 Some Probability Rules- Compound Events Independent Events - events where the occurrence or nonoccurrence of one does not For example: deck. Since you replaced it, the probabilities when you select the 2nd card do not change. the probabilities of your second selection would change. Dependent Events - when the outcome of the first event changes the probability of the next event. Does the independence or dependence of an event matter? Independence or dependence determines the way we compute probability of two For Independent Events For Dependent Events " " " Example: If you want to compute the probability of drawing an ace or a king on 2 It is important to distinguish between the"or" combinations and the"and" combinations because we apply different rules to compute the probabilities. Probability Rules: "OR" Problems - add "AND" Problems - multiply 1) Dice 2) Deck of 52 Cards Examples: 1) The probability of throwing two fours on a single toss of a pair of dice is a) 1/6 c) 1/12 d) 1/36 2) If two coins are tossed the probability of getting two tails is a) 1/8 c) 1/4 3) If two cards are drawn from a standard deck of 52 cards without replacement, what is the probability that both cards are fives? a) 4/52 3/52 b) 5/52 4/51 c) 1/4 1/3 d) 2/52 4) From a deck of 52 cards, two cards are randomly drawn without replacement. What is the probability of drawing two hearts? a) 13/52 12/51 b) 13/52 13/51 c) 2/52 d) 13/52 13/51 5) If two cards are drawn from a standard deck of 52 cards without replacement, what is the probability that both cards will be black aces? a) 2/52 2/51 b) 4/52 3/51 c) 4/52 4/51 d) 2/52 1/51 6) If 2 cards are dealt randomly from a standard deck of 52 cards, what is the probability that they are both red queens? a) 2/52 1/51 b) 2/26 c) 4/52 31/51 d) 2/52 7) From a standard deck of 52 cards, two cards are drawn at random without replacement. What is the probability that both cards drawn are aces? a) 12/2,652 b) 4/2,652 c) 4/52 d) 6/2,652 probability of obtaining, at random and without replacement, two yellow gumballs? b) 36/121 c) 30/121 are chosen at random without replacement, what is the probability that both marbles will be yellow? a) 3/14 b) 7/56 c) 1/3 drawn at random, what is the probability both are blue? a) 6/9 b) 30/72 c) 2/9 d) 30/81 7

8 If events are dependent, the occurrence of one event changes the probability of the The notation P(A B) is read the probability P(A, given B) equals the probability that occurred. 8

9 Examples 9

10 Combination of Several Events The addition rule for mutually exclusive events can be extended so that it applies to the situation in which we have more than two events that are mutually exclusive to all other events. 10

11 Summary 11

12 12

13 2. Multiplication Rule of Counting 3. Permutations 4. Combinations 13

14 a method of listing outcomes of an experiment consisting of a series of activities 14

15 15

16 possible outcomes for event E possible outcomes for the series of events E possible outcomes for event E then there are a total of This rule extends to outcomes created by a series of three, four, or more events. Just simply multiply the number of events to get the total number of outcomes for the series. Factorial Notation For any counting number ( ),! = ( 1)( 2) 1 0! = 1 1! = 1 16

17 Examples Evaluate 4! Evaluate 5! Evaluate 6! Evaluate 7! Jean is making sandwiches for a class picnic. She is using 4 different fillings with 2 different kinds of bread. How many different kinds of sandwiches can she make using one kind of filling on one kind of bread for each sandwich? On a restaurant menu, there are six sandwich choices and three beverage choices. How many different lunches may a person order consisting of one sandwich and one beverage? John has 6 pairs of pants and 3 shirts. How many possible outfits consisting of one shirt and one pair of pants can he select? alternative CD's, 1 country CD, 2 Jazz CD's, and 2 Pop CD's from which to choose. How many different combinations of CD's can be played? stripes, and all the other items are solid colors. If Josh will not wear stripes and checkered patterns together, how many different shirt and pants combinations can Josh wear? 17

18 Permutations: Permutation Permutations are especially useful when the order of the data is important. Therefore, we need to enter the data in this order: n n 18

19 Examples 1. Evaluate 7 P 3 2. Evaluate 4 P 3 3. Evaluate 9 P 2 4. Evaluate 8 P 4 5. Evaluate 10 P 3 6. How many different 4-letter arrangements can be formed using the letters of the word JUMP, if each letter is used only once? 7. How many different five-digit numbers can be formed from the digits 1,2,3,4, and 5 if each digit is used only once? 8. How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once? 9. All seven-digit telephone numbers in a town begin with 245. How many telephone numbers may be assigned in the town if the last four digits do not begin or end in a zero? 19

20 Combinations: Combinations In combination problems, order is not taken into consideration. Therefore, the difference between permutations and combinations is that in permutations we are considering groupings and in combinations we are considering only the number of 20

21 Examples 1. Evaluate 7 C 3 2. Evaluate 9 C 3 3. Evaluate 10 C 2 4. Evaluate 8 C 6 5. Evaluate 4 C 3 6. Find the number of combinations of 6 things taken 3 at a time. 7. How many different committees of 3 people can be chosen from a group of 9 people? 8. positions individual play while making the first selection, how many teams can be formed if 14 candidates try out and the coach selects 5 players? 9. of 22 songs can be selected? 21

22 22

23 23

### 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

### CH 13. Probability and Data Analysis

11.1: Find Probabilities and Odds 11.2: Find Probabilities Using Permutations 11.3: Find Probabilities Using Combinations 11.4: Find Probabilities of Compound Events 11.5: Analyze Surveys and Samples 11.6:

### 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,

### Conditional Probability Worksheet

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

### Conditional Probability Worksheet

Conditional Probability Worksheet P( A and B) P(A B) = P( B) Exercises 3-6, compute the conditional probabilities P( AB) and P( B A ) 3. P A = 0.7, P B = 0.4, P A B = 0.25 4. P A = 0.45, P B = 0.8, P A

### Use this information to answer the following questions.

1 Lisa drew a token out of the bag, recorded the result, and then put the token back into the bag. She did this 30 times and recorded the results in a bar graph. Use this information to answer the following

### 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 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

### 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.

### NAME DATE PERIOD. Study Guide and Intervention

9-1 Section Title The probability of a simple event is a ratio that compares the number of favorable outcomes to the number of possible outcomes. Outcomes occur at random if each outcome occurs by chance.

### Finite Mathematics MAT 141: Chapter 8 Notes

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

### 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

### 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

### Fundamental Counting Principle

11 1 Permutations and Combinations You just bought three pairs of pants and two shirts. How many different outfits can you make with these items? Using a tree diagram, you can see that you can make six

### 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

### 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

### 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

### 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

### 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

### Independent Events B R Y

. Independent Events Lesson Objectives Understand independent events. Use the multiplication rule and the addition rule of probability to solve problems with independent events. Vocabulary independent

### Mathematical Foundations HW 5 By 11:59pm, 12 Dec, 2015

1 Probability Axioms Let A,B,C be three arbitrary events. Find the probability of exactly one of these events occuring. Sample space S: {ABC, AB, AC, BC, A, B, C, }, and S = 8. P(A or B or C) = 3 8. note:

### Chapter 10 Practice Test Probability

Name: Class: Date: ID: A Chapter 0 Practice Test Probability Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the likelihood of the event given its

### 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

### 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.

### Name: 1. Match the word with the definition (1 point each - no partial credit!)

Chapter 12 Exam Name: Answer the questions in the spaces provided. If you run out of room, show your work on a separate paper clearly numbered and attached to this exam. SHOW ALL YOUR WORK!!! Remember

### 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

### Basic Probability Ideas. Experiment - a situation involving chance or probability that leads to results called outcomes.

Basic Probability Ideas Experiment - a situation involving chance or probability that leads to results called outcomes. Random Experiment the process of observing the outcome of a chance event Simulation

### 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

### 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,

### Unit 19 Probability Review

. What is sample space? All possible outcomes Unit 9 Probability Review 9. I can use the Fundamental Counting Principle to count the number of ways an event can happen. 2. What is the difference between

### 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

### 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

### Math 1116 Probability Lecture Monday Wednesday 10:10 11:30

Math 1116 Probability Lecture Monday Wednesday 10:10 11:30 Course Web Page http://www.math.ohio state.edu/~maharry/ Chapter 15 Chances, Probabilities and Odds Objectives To describe an appropriate sample

### 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

### 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.

### MATH-7 SOL Review 7.9 and Probability and FCP Exam not valid for Paper Pencil Test Sessions

MATH-7 SOL Review 7.9 and 7.0 - Probability and FCP Exam not valid for Paper Pencil Test Sessions [Exam ID:LV0BM Directions: Click on a box to choose the number you want to select. You must select all

### Math 14 Lecture Notes Ch. 3.3

3.3 Two Basic Rules of Probability If we want to know the probability of drawing a 2 on the first card and a 3 on the 2 nd card from a standard 52-card deck, the diagram would be very large and tedious

### 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

### 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

### Section Theoretical and Experimental Probability...Wks 3

Name: Class: Date: Section 6.8......Theoretical and Experimental Probability...Wks 3. Eight balls numbered from to 8 are placed in a basket. One ball is selected at random. Find the probability that it

### Probability. March 06, J. Boulton MDM 4U1. P(A) = n(a) n(s) Introductory Probability

Most people think they understand odds and probability. Do you? Decision 1: Pick a card Decision 2: Switch or don't Outcomes: Make a tree diagram Do you think you understand probability? Probability Write

### 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

### A Probability Work Sheet

A Probability Work Sheet October 19, 2006 Introduction: Rolling a Die Suppose Geoff is given a fair six-sided die, which he rolls. What are the chances he rolls a six? In order to solve this problem, we

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

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

### 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

### 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

### Week 1: Probability models and counting

Week 1: Probability models and counting Part 1: Probability model Probability theory is the mathematical toolbox to describe phenomena or experiments where randomness occur. To have a probability model

### 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,

### 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

### 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

### 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

### Pre-Calculus Multiple Choice Questions - Chapter S12

1 What is the probability of rolling a two on one roll of a fair, six-sided die? a 1/6 b 1/2 c 1/3 d 1/12 Pre-Calculus Multiple Choice Questions - Chapter S12 2 What is the probability of rolling an even

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

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

### 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

### 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

### Probability. The Bag Model

Probability The Bag Model Imagine a bag (or box) containing balls of various kinds having various colors for example. Assume that a certain fraction p of these balls are of type A. This means N = total

### Find the probability of an event by using the definition of probability

LESSON 10-1 Probability Lesson Objectives Find the probability of an event by using the definition of probability Vocabulary experiment (p. 522) trial (p. 522) outcome (p. 522) sample space (p. 522) event

### 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:

### 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

### 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

### 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,

### 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 0: Preparing for Advanced Algebra

Lesson 0-1: Representing Functions Date: Example 1: Locate Coordinates Name the quadrant in which the point is located. Example 2: Identify Domain and Range State the domain and range of each relation.

### RANDOM EXPERIMENTS AND EVENTS

Random Experiments and Events 18 RANDOM EXPERIMENTS AND EVENTS In day-to-day life we see that before commencement of a cricket match two captains go for a toss. Tossing of a coin is an activity and getting

### Math 7 Notes - Unit 7B (Chapter 11) Probability

Math 7 Notes - Unit 7B (Chapter 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

### 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

### 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

### Chapter 3: Elements of Chance: Probability Methods

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

### 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

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

166 CHAPTER 3 PROBABILITY TOPICS Raise your hand if you rode a bus within the past month. Record the number of raised hands. Raise your hand if you answered "yes" to BOTH of the first two questions. Record

### Applications. 28 How Likely Is It? P(green) = 7 P(yellow) = 7 P(red) = 7. P(green) = 7 P(purple) = 7 P(orange) = 7 P(yellow) = 7

Applications. A bucket contains one green block, one red block, and two yellow blocks. You choose one block from the bucket. a. Find the theoretical probability that you will choose each color. P(green)

### 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.

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

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

### 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:

### 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

### 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

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

North Seattle Community College Winter 2012 ELEMENTARY STATISTICS 2617 MATH 109 - Section 05, Practice Questions for Test 2 Chapter 3 and 4 1. Classify each statement as an example of empirical probability,

### PRE-CALCULUS PROBABILITY UNIT Permutations and Combinations Fundamental Counting Principal A way to find the total possible something can be arranged.

PRE-CALCULUS PROBABILITY UNIT Permutations and Combinations Fundamental Counting Principal A way to find the total possible something can be arranged. The lunch special at the local Greasy Spoon diner

### 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

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

Chapter 8: Probability: The Mathematics of Chance November 8, 2013 Last Time Probability Models and Rules Discrete Probability Models Equally Likely Outcomes Crystallographic notation The first symbol

### 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

### [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

### Honors Precalculus Chapter 9 Summary Basic Combinatorics

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

### Stat210 WorkSheet#2 Chapter#2

1. When rolling a die 5 times, the number of elements of the sample space equals.(ans.=7,776) 2. If an experiment consists of throwing a die and then drawing a letter at random from the English alphabet,

### Math 447 Test 1 February 25, Spring 2016

Math 447 Test 1 February 2, Spring 2016 No books, no notes, only scientific (non-graphic calculators. You must show work, unless the question is a true/false or fill-in-the-blank question. Name: Question

### Module 4 Project Maths Development Team Draft (Version 2)

5 Week Modular Course in Statistics & Probability Strand 1 Module 4 Set Theory and Probability It is often said that the three basic rules of probability are: 1. Draw a picture 2. Draw a picture 3. Draw

### 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

### 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.

### Name: Section: Date:

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

### The study of probability is concerned with the likelihood of events occurring. Many situations can be analyzed using a simplified model of probability

The study of probability is concerned with the likelihood of events occurring Like combinatorics, the origins of probability theory can be traced back to the study of gambling games Still a popular branch

### MATH STUDENT BOOK. 7th Grade Unit 6

MATH STUDENT BOOK 7th Grade Unit 6 Unit 6 Probability and Graphing Math 706 Probability and Graphing Introduction 3 1. Probability 5 Theoretical Probability 5 Experimental Probability 13 Sample Space 20

### Normal Distribution Lecture Notes Continued

Normal Distribution Lecture Notes Continued 1. Two Outcome Situations Situation: Two outcomes (for against; heads tails; yes no) p = percent in favor q = percent opposed Written as decimals p + q = 1 Why?

### 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

### #2. A coin is tossed 40 times and lands on heads 21 times. What is the experimental probability of the coin landing on tails?

1 Pre-AP Geometry Chapter 14 Test Review Standards/Goals: A.1.f.: I can find the probability of a simple event. F.1.c.: I can use area to solve problems involving geometric probability. S.CP.1: I can define

### 7.1 Chance Surprises, 7.2 Predicting the Future in an Uncertain World, 7.4 Down for the Count

7.1 Chance Surprises, 7.2 Predicting the Future in an Uncertain World, 7.4 Down for the Count Probability deals with predicting the outcome of future experiments in a quantitative way. The experiments

### 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

### Review of Probability

Review of Probability 1) What is probability? ( ) Consider the following two problems: Select 2 cards from a standard deck of 52 cards with replacement. What is the probability of obtaining two kings?