Math Tech IIII, Jan 21
|
|
- Ilene Daniel
- 6 years ago
- Views:
Transcription
1 Math Tech IIII, Jan 21 Probability III The Complement of an Event, Theoretical and Experimental Probability Book Sections: 3.1 Essential Questions: How can I compute the probability of any event? What is the compliment of and an event and what is its probability? What is the difference between probability theory and reality and how does it affect probability? Standards: DA-1.5, DA-5.5, DA-5.9, DA-5.7, S.CP.1
2 Complementary Events The compliment of an event A is everything happening except A The compliment of A is called not A and is abbreviated with A (called as A bar)
3 Examples The compliment of heads on a coin flip would be not heads - which would be tails The compliment of a 5 on a dice roll (not 5) - would be 1, 2, 3, 4, or 6 The compliment of a rainy day forecast for today - would be no rain today
4 Complementary Events An event will either happen or it will not. All possible outcomes that are not an event add up to be the compliment of that event. The sum of the probability of an event and the event s compliment always add up to 1 or P(event) + P(not the event) = 1, where P(not the event) is the probability of the event s compliment.
5 In Other Words The probability of a complimentary event is: P(event) = 1 P(event) or P(A) = 1 P(A) Example: What is the probability of not getting a 3 when rolling a die? 1 P(3) =
6 Examples
7 The Mathematical Definition of Probability One More Time P(event) = Number of favorable outcomes Total number of outcomes In words: The probability of an event is the ratio of favorable outcomes to the number of possible outcomes. That number will always be between 0 and 1.
8 The Basis of Probability Theory To date, every probabilistic model we have considered (dice, coins, spinners, cards, ect) has been based on what should happen if we had true random events and how we would compute probabilities. Probabilities that are based on known characteristics or facts are called theoretical probabilities, and that is what we have studied so far in this unit.
9 Types of Probability Theoretical Probability Probability based on a mathematical model, or what should happen in random events. Experimental Probability - Probability based on repetitions of an actual experiment, computed from the results of a lot of observations, or what actually happens in random events.
10 Computing Experimental Probability Experimental probability is computed from manymany actual observations P(event) = Number of favorable outcomes observed Total number of Trials
11 Theory Can Only Cover so Many Bases If we have complete knowledge of the set of possible outcomes of an event, then theoretical probability is a good predictor of what should happen. If we don t know how an experiment will behave or the outcome of event will occur, there is no way of predicting results based on theories, so we have to gain that knowledge by conducting the experiment many times.
12 Experimental Probability What it Means Experimental probability is a probability based on conducting an experiment over and over and can vary as the experiment is continually repeated.
13 An Example Over the last eight years, Farmer Jones has determined that only five out of six corn seeds planted on his 3000 acre farm produce corn. Is this theoretical or experimental probability? Experimental because it is based on what happened in the past. If Farmer Jones wants 10,000 corn-bearing plants, how many should he plant?
14 An Example Over the last eight years, Farmer Jones has determined that only five out of six corn seeds planted on his 3000 acre farm produce corn. Is this theoretical or experimental probability? Experimental because it is based on what happened in the past. If Farmer Jones wants 10,000 corn-bearing plants, how many should he plant? 5 of 6 seeds should produce corn ,000 x Set up the proportion 10,000 out of x seeds should produce corn or 5 x = 6 10,000, solving, x = 12,000 seeds
15 Example Two Quality control at a fan belt factory randomly selects 200 production belts a day and tests their quality. Over a ten day period, they have found a total of 15 defective fan belts. Experimental because it is based on sampling and testing (experimenting). What is the experimental probability that any given fan belt is defective from this factory?
16 Example Two, Answer What is the experimental probability that any given fan belt is defective from this factory? 200 belts/day 10 days = 2000 belts tested 15 bad out of 2000 = 15/2000 = 3/400 =.0075 The P(Bad Belt) =.0075 or.75% If the factory produces 25,000 belts every day, how many are defective? 25,000 x.0075 = or 188 bad belts Do you think the.75% probability is a constant?
17 Theoretical and Experimental Side-by Side 700 Trials of this spinner yield the following results: OC = Outcome OC Obs P(#) Theoretical P /140 (.136) /350 (.146) /7 (.143) /175 (.131) /70 (.129) /350 (.163) /700 (.153)
18 The Theory vs. Application Celebrity Death Match Does Theoretical Probability Match Experimental Probability? We shall see next time.
19 Class work: CW 1/21, All of it Homework: None
Math Tech IIII, Jan 16
Math Tech IIII, Jan 16 Probability IIII Theoretical and Experimental Probability & Compliments Book Sections: 3.1 Essential Questions: What is the difference between probability theory and reality and
More informationThe probability of an event is viewed as a numerical measure of the chance that the event will occur.
Chapter 5 This chapter introduces probability to quantify randomness. Section 5.1: How Can Probability Quantify Randomness? The probability of an event is viewed as a numerical measure of the chance that
More informationMath 140 Introductory Statistics
Math 140 Introductory Statistics 5.1 Models of random behavior Outcome: Result or answer obtained from a chance process. Event: Collection of outcomes. Probability: Number between 0 and 1 (0% and 100%).
More informationProbability Rules. MATH 130, Elements of Statistics I. J. Robert Buchanan. Fall Department of Mathematics
Probability Rules MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018 Introduction Probability is a measure of the likelihood of the occurrence of a certain behavior
More informationLecture notes for probability. Math 124
Lecture notes for probability Math 124 What is probability? Probabilities are ratios, expressed as fractions, decimals, or percents, determined by considering results or outcomes of experiments whose result
More informationProbability Notes. Definitions: The probability of an event is the likelihood of choosing an outcome from that event.
ability Notes Definitions: Sample Space: sample space is a set or collection of possible outcomes. Flipping a Coin: {Head, Tail} Rolling Two Die: {,,,, 6, 7, 8, 9, 0,, } Outcome: n outcome is an element
More informationSTAT 201 Chapter 5. Probability
STAT 201 Chapter 5 Probability 1 2 Introduction to Probability Probability The way we quantify uncertainty. Subjective Probability A probability derived from an individual's personal judgment about whether
More informationCh 14 Randomness and Probability
Ch 14 Randomness and Probability We ll begin a new part: randomness and probability. This part contain 4 chapters: 14-17. Why we need to learn this part? Probability is not a portion of statistics. Instead
More information4/17/2012. NE ( ) # of ways an event can happen NS ( ) # of events in the sample space
I. Vocabulary: A. Outcomes: the things that can happen in a probability experiment B. Sample Space (S): all possible outcomes C. Event (E): one outcome D. Probability of an Event (P(E)): the likelihood
More informationChap 4 Probability p227 The probability of any outcome in a random phenomenon is the proportion of times the outcome would occur in a long series of
Chap 4 Probability p227 The probability of any outcome in a random phenomenon is the proportion of times the outcome would occur in a long series of repetitions. (p229) That is, probability is a long-term
More informationBasic Concepts of Probability
Probability Probability theory is the branch of math that deals with random events Probability is used to describe how likely a particular outcome is in a random event the probability of obtaining heads
More informationMAT Mathematics in Today's World
MAT 1000 Mathematics in Today's World Last Time We discussed the four rules that govern probabilities: 1. Probabilities are numbers between 0 and 1 2. The probability an event does not occur is 1 minus
More informationMATH MW Elementary Probability Course Notes Part I: Models and Counting
MATH 2030 3.00MW Elementary Probability Course Notes Part I: Models and Counting Tom Salisbury salt@yorku.ca York University Winter 2010 Introduction [Jan 5] Probability: the mathematics used for Statistics
More informationChapter 6: Probability The Study of Randomness
Chapter 6: Probability The Study of Randomness 6.1 The Idea of Probability 6.2 Probability Models 6.3 General Probability Rules 1 Simple Question: If tossing a coin, what is the probability of the coin
More informationProbability- describes the pattern of chance outcomes
Chapter 6 Probability the study of randomness Probability- describes the pattern of chance outcomes Chance behavior is unpredictable in the short run, but has a regular and predictable pattern in the long
More informationFundamentals of Probability CE 311S
Fundamentals of Probability CE 311S OUTLINE Review Elementary set theory Probability fundamentals: outcomes, sample spaces, events Outline ELEMENTARY SET THEORY Basic probability concepts can be cast in
More informationMath 243 Section 3.1 Introduction to Probability Lab
Math 243 Section 3.1 Introduction to Probability Lab Overview Why Study Probability? Outcomes, Events, Sample Space, Trials Probabilities and Complements (not) Theoretical vs. Empirical Probability The
More informationStatistics for Engineers
Statistics for Engineers Antony Lewis http://cosmologist.info/teaching/stat/ Starter question Have you previously done any statistics? 1. Yes 2. No 54% 46% 1 2 BOOKS Chatfield C, 1989. Statistics for
More informationProblems from Probability and Statistical Inference (9th ed.) by Hogg, Tanis and Zimmerman.
Math 224 Fall 2017 Homework 1 Drew Armstrong Problems from Probability and Statistical Inference (9th ed.) by Hogg, Tanis and Zimmerman. Section 1.1, Exercises 4,5,6,7,9,12. Solutions to Book Problems.
More informationProbability deals with modeling of random phenomena (phenomena or experiments whose outcomes may vary)
Chapter 14 From Randomness to Probability How to measure a likelihood of an event? How likely is it to answer correctly one out of two true-false questions on a quiz? Is it more, less, or equally likely
More informationLecture 1 Introduction to Probability and Set Theory Text: A Course in Probability by Weiss
Lecture 1 to and Set Theory Text: A Course in by Weiss 1.2 2.3 STAT 225 to Models January 13, 2014 to and Whitney Huang Purdue University 1.1 Agenda to and 1 2 3 1.2 Motivation Uncertainty/Randomness in
More informationMath 493 Final Exam December 01
Math 493 Final Exam December 01 NAME: ID NUMBER: Return your blue book to my office or the Math Department office by Noon on Tuesday 11 th. On all parts after the first show enough work in your exam booklet
More information6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 Transcript Tutorial:A Random Number of Coin Flips
6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 Transcript Tutorial:A Random Number of Coin Flips Hey, everyone. Welcome back. Today, we're going to do another fun problem that
More informationAMS7: WEEK 2. CLASS 2
AMS7: WEEK 2. CLASS 2 Introduction to Probability. Probability Rules. Independence and Conditional Probability. Bayes Theorem. Risk and Odds Ratio Friday April 10, 2015 Probability: Introduction Probability:
More informationI - Probability. What is Probability? the chance of an event occuring. 1classical probability. 2empirical probability. 3subjective probability
What is Probability? the chance of an event occuring eg 1classical probability 2empirical probability 3subjective probability Section 2 - Probability (1) Probability - Terminology random (probability)
More informationPresentation on Theo e ry r y o f P r P o r bab a il i i l t i y
Presentation on Theory of Probability Meaning of Probability: Chance of occurrence of any event In practical life we come across situation where the result are uncertain Theory of probability was originated
More informationProbability: Part 1 Naima Hammoud
Probability: Part 1 Naima ammoud Feb 7, 2017 Motivation ossing a coin Rolling a die Outcomes: eads or ails Outcomes: 1, 2, 3, 4, 5 or 6 Defining Probability If I toss a coin, there is a 50% chance I will
More informationk P (X = k)
Math 224 Spring 208 Homework Drew Armstrong. Suppose that a fair coin is flipped 6 times in sequence and let X be the number of heads that show up. Draw Pascal s triangle down to the sixth row (recall
More informationgreen, green, green, green, green The favorable outcomes of the event are blue and red.
0 Chapter Review Review Key Vocabulary experiment, p. 0 outcomes, p. 0 event, p. 0 favorable outcomes, p. 0 probability, p. 08 relative frequency, p. Review Examples and Exercises experimental probability,
More informationECE 340 Probabilistic Methods in Engineering M/W 3-4:15. Lecture 2: Random Experiments. Prof. Vince Calhoun
ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Lecture 2: Random Experiments Prof. Vince Calhoun Reading This class: Section 2.1-2.2 Next class: Section 2.3-2.4 Homework: Assignment 1: From the
More informationChapter 7 Wednesday, May 26th
Chapter 7 Wednesday, May 26 th Random event A random event is an event that the outcome is unpredictable. Example: There are 45 students in this class. What is the probability that if I select one student,
More information2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 3 Probability Contents 1. Events, Sample Spaces, and Probability 2. Unions and Intersections 3. Complementary Events 4. The Additive Rule and Mutually Exclusive
More informationBasic Concepts of Probability
Probability Probability theory is the branch of math that deals with unpredictable or random events Probability is used to describe how likely a particular outcome is in a random event the probability
More informationProbability Long-Term Memory Review Review 1
Review. The formula for calculating theoretical probability of an event is What does the question mark represent? number of favorable outcomes P.? 2. True or False Experimental probability is always the
More informationSets and Set notation. Algebra 2 Unit 8 Notes
Sets and Set notation Section 11-2 Probability Experimental Probability experimental probability of an event: Theoretical Probability number of time the event occurs P(event) = number of trials Sample
More informationSTA 2023 EXAM-2 Practice Problems. Ven Mudunuru. From Chapters 4, 5, & Partly 6. With SOLUTIONS
STA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6 With SOLUTIONS Mudunuru, Venkateswara Rao STA 2023 Spring 2016 1 1. A committee of 5 persons is to be formed from 6 men and 4 women. What
More informationEvent A: at least one tail observed A:
Chapter 3 Probability 3.1 Events, sample space, and probability Basic definitions: An is an act of observation that leads to a single outcome that cannot be predicted with certainty. A (or simple event)
More informationP (A) = P (B) = P (C) = P (D) =
STAT 145 CHAPTER 12 - PROBABILITY - STUDENT VERSION The probability of a random event, is the proportion of times the event will occur in a large number of repititions. For example, when flipping a coin,
More information(6, 1), (5, 2), (4, 3), (3, 4), (2, 5), (1, 6)
Section 7.3: Compound Events Because we are using the framework of set theory to analyze probability, we can use unions, intersections and complements to break complex events into compositions of events
More informationIntroduction to probability
Introduction to probability 4.1 The Basics of Probability Probability The chance that a particular event will occur The probability value will be in the range 0 to 1 Experiment A process that produces
More informationProbability Year 9. Terminology
Probability Year 9 Terminology Probability measures the chance something happens. Formally, we say it measures how likely is the outcome of an event. We write P(result) as a shorthand. An event is some
More informationName: Exam 2 Solutions. March 13, 2017
Department of Mathematics University of Notre Dame Math 00 Finite Math Spring 07 Name: Instructors: Conant/Galvin Exam Solutions March, 07 This exam is in two parts on pages and contains problems worth
More informationSTA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6. With SOLUTIONS
STA 2023 EXAM-2 Practice Problems From Chapters 4, 5, & Partly 6 With SOLUTIONS Mudunuru Venkateswara Rao, Ph.D. STA 2023 Fall 2016 Venkat Mu ALL THE CONTENT IN THESE SOLUTIONS PRESENTED IN BLUE AND BLACK
More informationDiscrete Probability Distributions
Discrete Probability Distributions EGR 260 R. Van Til Industrial & Systems Engineering Dept. Copyright 2013. Robert P. Van Til. All rights reserved. 1 What s It All About? The behavior of many random processes
More informationProbability and Independence Terri Bittner, Ph.D.
Probability and Independence Terri Bittner, Ph.D. The concept of independence is often confusing for students. This brief paper will cover the basics, and will explain the difference between independent
More informationSTA 291 Lecture 8. Probability. Probability Rules. Joint and Marginal Probability. STA Lecture 8 1
STA 291 Lecture 8 Probability Probability Rules Joint and Marginal Probability STA 291 - Lecture 8 1 Union and Intersection Let A and B denote two events. The union of two events: A B The intersection
More informationChapter 2 PROBABILITY SAMPLE SPACE
Chapter 2 PROBABILITY Key words: Sample space, sample point, tree diagram, events, complement, union and intersection of an event, mutually exclusive events; Counting techniques: multiplication rule, permutation,
More informationMath 1313 Experiments, Events and Sample Spaces
Math 1313 Experiments, Events and Sample Spaces At the end of this recording, you should be able to define and use the basic terminology used in defining experiments. Terminology The next main topic in
More information3.2 Probability Rules
3.2 Probability Rules The idea of probability rests on the fact that chance behavior is predictable in the long run. In the last section, we used simulation to imitate chance behavior. Do we always need
More informationCompound Events. The event E = E c (the complement of E) is the event consisting of those outcomes which are not in E.
Compound Events Because we are using the framework of set theory to analyze probability, we can use unions, intersections and complements to break complex events into compositions of events for which it
More informationUnit 7 Probability M2 13.1,2,4, 5,6
+ Unit 7 Probability M2 13.1,2,4, 5,6 7.1 Probability n Obj.: I will be able to determine the experimental and theoretical probabilities of an event, or its complement, occurring. n Vocabulary o Outcome
More informationProbability, Conditional Probability and Bayes Rule IE231 - Lecture Notes 3 Mar 6, 2018
Probability, Conditional Probability and Bayes Rule IE31 - Lecture Notes 3 Mar 6, 018 #Introduction Let s recall some probability concepts. Probability is the quantification of uncertainty. For instance
More informationBasic Concepts of Probability. Section 3.1 Basic Concepts of Probability. Probability Experiments. Chapter 3 Probability
Chapter 3 Probability 3.1 Basic Concepts of Probability 3.2 Conditional Probability and the Multiplication Rule 3.3 The Addition Rule 3.4 Additional Topics in Probability and Counting Section 3.1 Basic
More informationProbability and Sample space
Probability and Sample space We call a phenomenon random if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions. The probability of any outcome
More informationProbability Year 10. Terminology
Probability Year 10 Terminology Probability measures the chance something happens. Formally, we say it measures how likely is the outcome of an event. We write P(result) as a shorthand. An event is some
More informationSection 4.2 Basic Concepts of Probability
Section 4.2 Basic Concepts of Probability 2012 Pearson Education, Inc. All rights reserved. 1 of 88 Section 4.2 Objectives Identify the sample space of a probability experiment Identify simple events Use
More informationA brief review of basics of probabilities
brief review of basics of probabilities Milos Hauskrecht milos@pitt.edu 5329 Sennott Square robability theory Studies and describes random processes and their outcomes Random processes may result in multiple
More information6.2 Introduction to Probability. The Deal. Possible outcomes: STAT1010 Intro to probability. Definitions. Terms: What are the chances of?
6.2 Introduction to Probability Terms: What are the chances of?! Personal probability (subjective) " Based on feeling or opinion. " Gut reaction.! Empirical probability (evidence based) " Based on experience
More informationProperties of Probability
Econ 325 Notes on Probability 1 By Hiro Kasahara Properties of Probability In statistics, we consider random experiments, experiments for which the outcome is random, i.e., cannot be predicted with certainty.
More informationUniversity of California, Berkeley, Statistics 134: Concepts of Probability. Michael Lugo, Spring Exam 1
University of California, Berkeley, Statistics 134: Concepts of Probability Michael Lugo, Spring 2011 Exam 1 February 16, 2011, 11:10 am - 12:00 noon Name: Solutions Student ID: This exam consists of seven
More information5.5 PROBABILITY AS A THEORETICAL CONCEPT
5.5 PROAILIY AS A EOREICAL CONCEP So far, we have solved probability problems by estimating the required probability after conducting some sort of experiment and collecting data. ut probability may be
More informationProbability & Random Variables
& Random Variables Probability Probability theory is the branch of math that deals with random events, processes, and variables What does randomness mean to you? How would you define probability in your
More informationLecture 5: Introduction to Markov Chains
Lecture 5: Introduction to Markov Chains Winfried Just Department of Mathematics, Ohio University January 24 26, 2018 weather.com light The weather is a stochastic process. For now we can assume that this
More informationMath 140 Introductory Statistics
5. Models of Random Behavior Math 40 Introductory Statistics Professor Silvia Fernández Chapter 5 Based on the book Statistics in Action by A. Watkins, R. Scheaffer, and G. Cobb. Outcome: Result or answer
More informationTheoretical Probability (pp. 1 of 6)
Theoretical Probability (pp. 1 of 6) WHAT ARE THE CHANCES? Objectives: Investigate characteristics and laws of probability. Materials: Coin, six-sided die, four-color spinner divided into equal sections
More informationMath 140 Introductory Statistics
Math 140 Introductory Statistics Professor Silvia Fernández Lecture 8 Based on the book Statistics in Action by A. Watkins, R. Scheaffer, and G. Cobb. 5.1 Models of Random Behavior Outcome: Result or answer
More informationChapter 5 : Probability. Exercise Sheet. SHilal. 1 P a g e
1 P a g e experiment ( observing / measuring ) outcomes = results sample space = set of all outcomes events = subset of outcomes If we collect all outcomes we are forming a sample space If we collect some
More informationSDS 321: Introduction to Probability and Statistics
SDS 321: Introduction to Probability and Statistics Lecture 2: Conditional probability Purnamrita Sarkar Department of Statistics and Data Science The University of Texas at Austin www.cs.cmu.edu/ psarkar/teaching
More informationP(A) = Definitions. Overview. P - denotes a probability. A, B, and C - denote specific events. P (A) - Chapter 3 Probability
Chapter 3 Probability Slide 1 Slide 2 3-1 Overview 3-2 Fundamentals 3-3 Addition Rule 3-4 Multiplication Rule: Basics 3-5 Multiplication Rule: Complements and Conditional Probability 3-6 Probabilities
More informationTopic 2 Probability. Basic probability Conditional probability and independence Bayes rule Basic reliability
Topic 2 Probability Basic probability Conditional probability and independence Bayes rule Basic reliability Random process: a process whose outcome can not be predicted with certainty Examples: rolling
More informationIndependence Solutions STAT-UB.0103 Statistics for Business Control and Regression Models
Independence Solutions STAT-UB.003 Statistics for Business Control and Regression Models The Birthday Problem. A class has 70 students. What is the probability that at least two students have the same
More informationHomework (due Wed, Oct 27) Chapter 7: #17, 27, 28 Announcements: Midterm exams keys on web. (For a few hours the answer to MC#1 was incorrect on
Homework (due Wed, Oct 27) Chapter 7: #17, 27, 28 Announcements: Midterm exams keys on web. (For a few hours the answer to MC#1 was incorrect on Version A.) No grade disputes now. Will have a chance to
More informationCISC 1100/1400 Structures of Comp. Sci./Discrete Structures Chapter 7 Probability. Outline. Terminology and background. Arthur G.
CISC 1100/1400 Structures of Comp. Sci./Discrete Structures Chapter 7 Probability Arthur G. Werschulz Fordham University Department of Computer and Information Sciences Copyright Arthur G. Werschulz, 2017.
More information4. Probability of an event A for equally likely outcomes:
University of California, Los Angeles Department of Statistics Statistics 110A Instructor: Nicolas Christou Probability Probability: A measure of the chance that something will occur. 1. Random experiment:
More informationUNIT 5 ~ Probability: What Are the Chances? 1
UNIT 5 ~ Probability: What Are the Chances? 1 6.1: Simulation Simulation: The of chance behavior, based on a that accurately reflects the phenomenon under consideration. (ex 1) Suppose we are interested
More informationDiscrete Probability
Discrete Probability Mark Muldoon School of Mathematics, University of Manchester M05: Mathematical Methods, January 30, 2007 Discrete Probability - p. 1/38 Overview Mutually exclusive Independent More
More informationMarquette University MATH 1700 Class 5 Copyright 2017 by D.B. Rowe
Class 5 Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science Copyright 2017 by D.B. Rowe 1 Agenda: Recap Chapter 3.2-3.3 Lecture Chapter 4.1-4.2 Review Chapter 1 3.1 (Exam
More informationEPE / EDP 557 Homework 7
Section III. A. Questions EPE / EDP 557 Homework 7 Section III. A. and Lab 7 Suppose you roll a die once and flip a coin twice. Events are defined as follows: A = {Die is a 1} B = {Both flips of the coin
More information9/6/2016. Section 5.1 Probability. Equally Likely Model. The Division Rule: P(A)=#(A)/#(S) Some Popular Randomizers.
Chapter 5: Probability and Discrete Probability Distribution Learn. Probability Binomial Distribution Poisson Distribution Some Popular Randomizers Rolling dice Spinning a wheel Flipping a coin Drawing
More informationChapter 14. From Randomness to Probability. Copyright 2012, 2008, 2005 Pearson Education, Inc.
Chapter 14 From Randomness to Probability Copyright 2012, 2008, 2005 Pearson Education, Inc. Dealing with Random Phenomena A random phenomenon is a situation in which we know what outcomes could happen,
More informationRULES OF PROBABILITY
RULES OF PROBABILITY COMPLEMENTARY EVENTS: Consider any event A. Let p(a) be the probability that A happens and let p(a ) read as the probability of A prime or A c (A Complement), be the probability that
More informationChapter 6. Probability
Chapter 6 robability Suppose two six-sided die is rolled and they both land on sixes. Or a coin is flipped and it lands on heads. Or record the color of the next 20 cars to pass an intersection. These
More informationExample. What is the sample space for flipping a fair coin? Rolling a 6-sided die? Find the event E where E = {x x has exactly one head}
Chapter 7 Notes 1 (c) Epstein, 2013 CHAPTER 7: PROBABILITY 7.1: Experiments, Sample Spaces and Events Chapter 7 Notes 2 (c) Epstein, 2013 What is the sample space for flipping a fair coin three times?
More informationLECTURE NOTES by DR. J.S.V.R. KRISHNA PRASAD
.0 Introduction: The theory of probability has its origin in the games of chance related to gambling such as tossing of a coin, throwing of a die, drawing cards from a pack of cards etc. Jerame Cardon,
More informationSection 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.
More informationSTP 226 ELEMENTARY STATISTICS
STP 226 ELEMENTARY STATISTICS CHAPTER 5 Probability Theory - science of uncertainty 5.1 Probability Basics Equal-Likelihood Model Suppose an experiment has N possible outcomes, all equally likely. Then
More informationChapter 4 Probability
4-1 Review and Preview Chapter 4 Probability 4-2 Basic Concepts of Probability 4-3 Addition Rule 4-4 Multiplication Rule: Basics 4-5 Multiplication Rule: Complements and Conditional Probability 4-6 Counting
More informationRandom Variable. Discrete Random Variable. Continuous Random Variable. Discrete Random Variable. Discrete Probability Distribution
Random Variable Theoretical Probability Distribution Random Variable Discrete Probability Distributions A variable that assumes a numerical description for the outcome of a random eperiment (by chance).
More informationToday we ll discuss ways to learn how to think about events that are influenced by chance.
Overview Today we ll discuss ways to learn how to think about events that are influenced by chance. Basic probability: cards, coins and dice Definitions and rules: mutually exclusive events and independent
More informationChapter 2. Probability. Math 371. University of Hawai i at Mānoa. Summer 2011
Chapter 2 Probability Math 371 University of Hawai i at Mānoa Summer 2011 W. DeMeo (williamdemeo@gmail.com) Chapter 2: Probability math.hawaii.edu/ williamdemeo 1 / 8 Outline 1 Chapter 2 Examples Definition
More informationProbability, For the Enthusiastic Beginner (Exercises, Version 1, September 2016) David Morin,
Chapter 8 Exercises Probability, For the Enthusiastic Beginner (Exercises, Version 1, September 2016) David Morin, morin@physics.harvard.edu 8.1 Chapter 1 Section 1.2: Permutations 1. Assigning seats *
More informationWhy should you care?? Intellectual curiosity. Gambling. Mathematically the same as the ESP decision problem we discussed in Week 4.
I. Probability basics (Sections 4.1 and 4.2) Flip a fair (probability of HEADS is 1/2) coin ten times. What is the probability of getting exactly 5 HEADS? What is the probability of getting exactly 10
More informationChapter. Probability
Chapter 3 Probability Section 3.1 Basic Concepts of Probability Section 3.1 Objectives Identify the sample space of a probability experiment Identify simple events Use the Fundamental Counting Principle
More informationAxioms of Probability
Sample Space (denoted by S) The set of all possible outcomes of a random experiment is called the Sample Space of the experiment, and is denoted by S. Example 1.10 If the experiment consists of tossing
More informationLecture 3 Probability Basics
Lecture 3 Probability Basics Thais Paiva STA 111 - Summer 2013 Term II July 3, 2013 Lecture Plan 1 Definitions of probability 2 Rules of probability 3 Conditional probability What is Probability? Probability
More informationLecture 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 4 times? Figure below shows the results of tossing a coin 5000 times twice.
More informationMATH 3C: MIDTERM 1 REVIEW. 1. Counting
MATH 3C: MIDTERM REVIEW JOE HUGHES. Counting. Imagine that a sports betting pool is run in the following way: there are 20 teams, 2 weeks, and each week you pick a team to win. However, you can t pick
More informationEvents A and B are said to be independent if the occurrence of A does not affect the probability of B.
Independent Events Events A and B are said to be independent if the occurrence of A does not affect the probability of B. Probability experiment of flipping a coin and rolling a dice. Sample Space: {(H,
More informationSection 2.4 Bernoulli Trials
Section 2.4 Bernoulli Trials A bernoulli trial is a repeated experiment with the following properties: 1. There are two outcomes of each trial: success and failure. 2. The probability of success in each
More informationSTOR Lecture 4. Axioms of Probability - II
STOR 435.001 Lecture 4 Axioms of Probability - II Jan Hannig UNC Chapel Hill 1 / 23 How can we introduce and think of probabilities of events? Natural to think: repeat the experiment n times under same
More information