Probability for Dummies / Deborah J. Rumsey.

Format:

Book

Author/Creator:

Rumsey, Deborah J. (Deborah Jean), 1961- author.

Series:

--For dummies.

For dummies.

Language:

English

Subjects (All):

Probabilities.

Physical Description:

1 online resource (403 pages)

Edition:

Second edition.

Place of Publication:

Hoboken, NJ : John Wiley & Sons, Inc., [2025]

Summary:

Learn how to calculate your chances with easy-to-understand explanations of probability. Probability—the likelihood or chance of an event occurring—is an important branch of mathematics used in business and economics, finance, engineering, physics, and beyond. We see probability at work every day in areas such as weather forecasting, investing, and sports betting. Packed with real-life examples and mathematical problems with thorough explanations, Probability For Dummies helps students, professionals, and the everyday reader learn the basics. Topics include set theory, counting, permutations and combinations, random variables, conditional probability, joint distributions, conditional expectations, and probability modeling. Pass your probability class and play your cards right, with this accessible Dummies guide.

Contents:

Intro

Title Page

Copyright Page

Table of Contents

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Beyond the Book

Where to Go from Here

Part 1 The Certainty of Uncertainty: Probability Basics

Chapter 1 The Probability in Everyday Life

Figuring Out What Probability Means

Understanding the concept of chance

Interpreting probabilities: Thinking large and long term

Playing the instant lottery

Pondering political affiliation

Seeing probability in everyday life

Coming Up with Probabilities

Be subjective

Take a classical approach

Find relative frequencies

Use simulations

Probability Misconceptions to Avoid

Thinking in 50-50 terms when you have two outcomes

Thinking that patterns can't occur

Picking a number from one to ten

Flipping a coin ten times

Chapter 2 Coming to Terms with Probability

A Set Notation Overview

Noting outcomes: Sample spaces

Finite samples spaces

Countably infinite sample spaces

Uncountably infinite sample spaces

Noting subsets of sample spaces: Events

Noting a void in the set: Empty sets

Putting sets together: Unions, intersections, and complements

Unions

Intersections

Complements

Probabilities of Events Involving A and/or B

Probability notation

Marginal probabilities

Union probabilities

Intersection (joint) probabilities

Complement probabilities

Conditional probabilities

Solving conditional probabilities without a formula

Solving conditional probabilities with a formula

Understanding and Applying the Rules of Probability

The complement rule (for opposites that don't attract)

The multiplication rule (for intersections, not for rabbits)

The addition rule (for unions of the nonmarital nature)

Recognizing Independence in Multiple Events.

Checking independence for two events with the definition

Utilizing the multiplication rule for independent events

Including Mutually Exclusive Events

Recognizing mutually exclusive events

Simplifying the addition rule with mutually exclusive events

Distinguishing Independent from Mutually Exclusive Events

Comparing and contrasting independence and mutual exclusivity

Checking for independence or exclusivity in a 52-card deck

Getting Some Practice

Solutions

Chapter 3 Picturing Probability: Venn Diagrams, Tree Diagrams, and Bayes' Theorem

Diagramming Probabilities with Venn Diagrams

Using Venn diagrams to find probabilities beyond those given

Using Venn diagrams to organize and visualize relationships

Proving intermediate rules about sets using Venn diagrams

Exploring the limitations of Venn diagrams

Mapping Out Probabilities with Tree Diagrams

Showing multistage outcomes with a tree diagram

Organizing conditional probabilities with a tree diagram

Organizing probabilities for independent events

Organizing probabilities for dependent events

Connecting the tree's branches to the rules of probability

Drawing a tree diagram to find probabilities for complex events

Example 1: The probability of choosing exactly one female

Example 2: The probability of choosing at least one female

Example 3: The probability that both people you choose have the same gender

The Law of Total Probability and Bayes' Theorem

Finding a marginal probability using the Law of Total Probability

Formalizing the Law of Total Probability

Setting up the tree diagram

Plugging in the probabilities

Putting probabilities together to find the total probability

Finding the posterior probability with Bayes' Theorem

Formalizing Bayes' Theorem.

Setting up the tree diagram and putting in the probabilities

Answering Question 1: Finding the posterior probability

Answering Question 2: Which restaurant did the satisfied customer most likely go to?

Part 2 Counting on Probability and Betting to Win

Chapter 4 Setting the Contingency Table with Probabilities

Organizing a Contingency Table

Defining the sample space

Setting up the rows and columns

Inserting the data

Adding the row, column, and grand totals

Finding and Interpreting Probabilities within a Contingency Table

Figuring joint probabilities

Calculating marginal probabilities

Identifying conditional probabilities

Checking for Independence of Two Events

Chapter 5 Applying Counting Rules with Combinations and Permutations

Counting on Permutations

Unraveling a permutation

Permutation problems with added restrictions: Are we having fun yet?

Certain items can't be placed next to each other

Certain items are distinct

others are not

Rearranging items in a circle versus a straight line

Choosing items with no repeats allowed when order matters

Choosing numbers when order matters and repeats are allowed

Finding probabilities involving permutations

Choosing your words carefully: Splitting out the numerator and denominator

Getting people lined up: Looking for the hidden subtleties of each problem

Counting Combinations

Solving combination problems

Combinations and Pascal's triangle

Probability problems involving combinations

Splitting objects or individuals into two groups

Picking items in any order with no repeats allowed

Picking items in any order with repeats allowed

Studying more complex combinations through poker hands

Ranking poker hands.

Figuring the number of ways to draw each poker hand

Hitting four of a kind

Finding probabilities involving combinations

Choosing with restrictions

Calculating probabilities for poker hands

Grouping and regrouping

Chapter 6 Against All Odds: Probability in Gaming

Knowing Your Chances: Probability, Odds, and Expected Value

Playing the Lottery

Mulling the probability of winning the lottery

Pick three

Powerball

Figuring the odds

Finding the expected value of a lottery ticket

Expected value of a pick-three ticket

Expected value of a Powerball ticket

Hitting the Slot Machines

Understanding average payout

Unraveling slot machine myths

Slot machines stop on all possible outcomes with equal probability

Someone immediately hits a jackpot after you leave a machine

you would've won that pot had you stayed

Machines are programmed to "heat up" during certain times

If you've been sitting at a machine that hasn't won in a long time, stay with it - it's due to hit soon

Machines set up in different places in the casino have better payouts

Implementing a simple strategy for slots

Choosing among nickel, quarter, and dollar machines

Deciding how many coins to play at a time

Spinning the Roulette Wheel

Covering roulette-wheel basics

Making outside and inside bets

Placing an outside bet

Placing an inside bet

Chances and expected payouts on roulette bets

Developing a roulette strategy

Getting Your Chance to Yell "Bingo!"

Ways to win at bingo

The probability of getting bingo - it's more complicated than you may think

Finding the total cards possible in bingo

Finding the odds of getting bingo

Knowing What You're Up Against: Gambler's Ruin

The Famous Birthday Problem.

Part 3 From A to Binomial: Basic Probability Models

Chapter 7 Probability Distribution Basics

The Probability Distribution of a Discrete Random Variable

Defining a random variable

Finding and using the probability distribution

Picturing probability distributions: Plotting on a histogram

Calculating probabilities in the discrete case: "At most," "at least," and more

Finding and Using the Cumulative Distribution Function

Interpreting the cdf

Graphing the cdf

Finding probabilities with the cdf

Exploring less-than, greater-than, or less-than or equal-to/greater-than or equal-to probabilities

Exploring between-values probabilities

Determining the pmf given the cdf

Expected Value, Variance, and Standard Deviation of a Discrete Random Variable

Finding the expected value of X

Calculating the variance of X

Finding the standard deviation of X

Outlining the Discrete Uniform Distribution

The pmf of the discrete uniform

The cdf of the discrete uniform

The expected value of the discrete uniform

The variance and standard deviation of the discrete uniform

Chapter 8 Juggling Success and Failure with the Binomial Distribution

Recognizing the Binomial Model

Checking the binomial conditions step-by-step

Spotting a variable that isn't binomial

Surveying the number of trials: Fixed or not?

Sampling without replacement: Does it change p?

Finding Probabilities for the Binomial

Finding binomial probabilities with the pmf

Putting the pmf formula into action

Picturing the binomial pmf

Finding binomial probabilities with the cdf

Understanding the cdf

Taking advantage of the table for the binomial cdf

Graphing the binomial cdf

Formulating the Expected Value and Variance of the Binomial

The expected value of the binomial.

The variance and standard deviation of the binomial.

Notes:

Includes index.

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

Description based on print version record.

ISBN:

9781394281893

1394281897

9781394281909

1394281900

OCLC:

1477820356