Probability For Dummies

Probability For Dummies
Table of Contents
Introduction
About This Book
Conventions Used in This Book
What You’re Not to Read
Foolish Assumptions
How This Book Is Organized
Icons Used in This Book
Where to Go from Here
Chapter 1: The Probability in Everyday Life
Figuring Out what Probability Means
Coming Up with Probabilities
Probability Misconceptions to Avoid
Chapter 2: Coming to Terms with Probability
A Set Notation Overview
Probabilities of Events Involving A and/or B
Understanding and Applying the Rules of Probability
Recognizing Independence in Multiple Events
Including Mutually Exclusive Events
Distinguishing Independent from Mutually Exclusive Events
Chapter 3: Picturing Probability: Venn Diagrams, Tree Diagrams, and Bayes’ Theorem
Diagramming Probabilities with Venn Diagrams
Mapping Out Probabilities with Tree Diagrams
The Law of Total Probability and Bayes’ Theorem
Chapter 4: Setting the Contingency Table with Probabilities
Organizing a Contingency Table
Finding and Interpreting Probabilities within a Contingency Table
Checking for Independence of Two Events
Chapter 5: Applying Counting Rules with Combinations and Permutations
Counting on Permutations
Counting Combinations
Chapter 6: Against All Odds: Probability in Gaming
Knowing Your Chances: Probability, Odds, and Expected Value
Playing the Lottery
Hitting the Slot Machines
Spinning the Roulette Wheel
Getting Your Chance to Yell “ BINGO!”
Knowing What You’re Up Against: Gambler’s Ruin
The Famous Birthday Problem
Chapter 7: Probability Distribution Basics
The Probability Distribution of a Discrete Random Variable
Finding and Using the Cumulative Distribution Function (cdf)
Expected Value, Variance, and Standard Deviation of a Discrete Random Variable
Outlining the Discrete Uniform Distribution
Chapter 8: Juggling Success and Failure with the Binomial Distribution
Recognizing the Binomial Model
Finding Probabilities for the Binomial
Formulating the Expected Value and Variance of the Binomial
Chapter 9: The Normal (but Never Dull) Distribution
Charting the Basics of the Normal Distribution
Finding and Using Probabilities for a Normal Distribution
Handling Backwards Normal Problems
Chapter 10: Approximating a Binomial with a Normal Distribution
Identifying When You Need to Approximate Binomials
Why the Normal Approximation Works when n Is Large Enough
Understanding the Normal Approximation to the Binomial
Approximating a Binomial Probability with the Normal: A Coin Example
Chapter 11: Sampling Distributions and the Central Limit Theorem
Surveying a Sampling Distribution
Gaining Access to Your Statistics through the Central Limit Theorem (CLT)
The Sampling Distribution of the Sample Total (t)
The Sampling Distribution of the Sample Mean, X
The Sampling Distribution of the Sample Proportion, p
Chapter 12: Investigating and Making Decisions with Probability
Confidence Intervals and Probability
Probability and Hypothesis Testing
Probability in Quality Control
Chapter 13: Working with the Poisson (a Nonpoisonous) Distribution
Counting On Arrivals with the Poisson Model
Determining Probabilities for the Poisson
Identifying the Expected Value and Variance of the Poisson
Changing Units Over Time or Space: The Poisson Process
Approximating a Poisson with a Normal
Chapter 14: Covering All the Angles of the Geometric Distribution
Shaping Up the Geometric Distribution
Finding Probabilities for the Geometric by Using the pmf
Uncovering the Expected Value and Variance of the Geometric
Chapter 15: Making a Positive out of the Negative Binomial Distribution
Recognizing the Negative Binomial Model
Formulating Probabilities for the Negative Binomial
Exploring the Expected Value and Variance of the Negative Binomial
Chapter 16: Remaining Calm about the Hypergeometric Distribution
Zooming In on the Conditions for the Hypergeometric Model
Finding Probabilities for the Hypergeometric Model
Measuring the Expected Value and Variance of the Hypergeometric
Chapter 17: Staying in Line with the Continuous Uniform Distribution
Understanding the Continuous Uniform Distribution
Determining the Density Function for the Continuous Uniform Distribution
Drawing Up Probabilities for the Continuous Uniform Distribution
Corralling Cumulative Probabilities, Using F(x)
Figuring the Expected Value and Variance of the Continuous Uniform
Chapter 18: The Exponential (and Its Relationship to Poisson) Exposed
Identifying the Density Function for the Exponential
Determining Probabilities for the Exponential
Figuring Formulas for the Expected Value and Variance of the Exponential
Relating the Poisson and Exponential Distributions
Chapter 19: Ten Steps to a Better Probability Grade
Get Into the Problem
Understand the Question
Organize the Information
Write Down the Formula You Need
Check the Conditions
Calculate with Confidence
Show Your Work
Check Your Answer
Interpret Your Results
Make a Review Sheet
Chapter 20: Top Ten (Plus One) Probability Mistakes
Forgetting a Probability Must Be Between Zero and One
Misinterpreting Small Probabilities
Using Probability for Short-Term Predictions
Thinking That 1-2-3-4-5-6 Can’t Win
“Keep ’em Coming . . . I’m on a Roll!”
Giving Every Situation a 50-50 Chance
Switching Conditional Probabilities Around
Applying the Wrong Probability Distribution
Leaving Probability Model Conditions Unchecked
Confusing Permutations and Combinations
Assuming Independence
Appendix: Tables for Your Reference
Binomial Table
Normal Table
Poisson Table
Index