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Robert Tier - Probability with Permutations and Combinations: A Deeper and More Thorough Look at the Fundamental Equations

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Robert Tier Probability with Permutations and Combinations: A Deeper and More Thorough Look at the Fundamental Equations
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Probability with Permutations and Combinations

A Deeper and More Thorough Look at the Fundamental Equations

By Robert Tier

Table of Contents

Copyright 2017 by Robert Tier - All rights reserved.

The following eBook is reproduced below with the goal of providing information that is as accurate and reliable as possible. Regardless, purchasing this eBook can be seen as consent to the fact that both the publisher and the author of this book are in no way experts on the topics discussed within and that any recommendations or suggestions that are made herein are for entertainment and/or educational purposes only. Professionals should be consulted as needed prior to undertaking any of the action endorsed herein.

This declaration is deemed fair and valid by both the American Bar Association and the Committee of Publishers Association and is legally binding throughout the United States.

Furthermore, the transmission, duplication or reproduction of any of the following work including specific information will be considered an illegal act irrespective of if it is done electronically or in print. This extends to creating a secondary or tertiary copy of the work or a recorded copy and is only allowed with express written consent from the Publisher. All additional right reserved.

The information in the following pages is broadly considered to be a truthful and accurate account of facts and as such any inattention, use or misuse of the information in question by the reader will render any resulting actions solely under their purview. There are no scenarios in which the publisher or the original author of this work can be in any fashion deemed liable for any hardship or damages that may befall them after undertaking information described herein.

Additionally, the information in the following pages is intended only for informational purposes and should thus be thought of as universal. As befitting its nature, it is presented without assurance regarding its prolonged validity or interim quality. Trademarks that are mentioned are done without written consent and can in no way be considered an endorsement from the trademark holder.

Introduction

Congratulations on downloading Probability with Permutations and Combinations: A Deeper and More Thorough Look at the Fundamental Equations and thank you for doing so.

The following chapters will discuss, firstly, the essential concepts underlying this entire book: probability, as well as permutations and combinations and how they complement it. Well be going into detail as to the essential equations which make up these concepts and the most important things to bear in mind as you work with them. Youll learn mental shortcuts, if you will; handy ways to think about these equations which will make them far easier to understand as you go forward.

Then, after discussing those essential concepts and equations, were going to focus a lot more on practical applicability. In fact, practical application is whats going to make up the vast majority of this book. Theres one primary reason for this: I dont know about you, but I think about math and the sciences in a peculiar way. I mean, sure, you can learn the underlying concepts. But really, what do you actually accomplish by thinking and not DOING.

There may be myriad reasons for why youre looking into this book. You may be looking for help understanding the difficult content of an algebra or statistics class. You may be learning how to use probability and statistics to your advantage for practical reasons such as advancing your career. You may be starting a business and looking to use probability and related statistical analytics in order to increase your performance and make it so that you take a mathematical approach to certain things like sales and marketing (which will certainly give you a leg up over your competitors).

Regardless of your exact intent, I can almost assure you that you're going to find what you're looking for in this book: an easy in-depth explanation of not only probability but also permutations and combinations, as well as how these concepts can be used in different practical applications in your day-to-day life.

What makes this book better than others on the market? The problem with these books is that all too often, they are bad in one of two ways.

The first way is that they cover a ton of content and never really zero in on a specific concept. This is the kind of learning you'd get from a bigger math textbook. This is great if you want a brief summary of a concept or a textbook definition of usage, or a certain formula; but as far as actually understanding the concept or knowing how to use it practically? Good luck.

And as for the other way: there are a lot of books out there that get too simple and too specific. And these books, much like the others, fail to teach effectively the concepts in question, but for an entirely different reason. These books fail to properly address enough situations so that you can see the multiple ways in which such a broad concept as probability can be used, especially the extremely useful extensions of permutations and combinations.

So I invite you to put your math fedora on and get ready to learn real-world applications of some of the most useful equations to date! Every effort was made to ensure it is full of as much useful information as possible, please enjoy! I'm certain that you won't regret it.

Chapter 1: What is probability?

I suppose that this really is a better starting place than any. What is probability? Im sure the answer is obvious, but its important for the flow and nature of the book that we establish what exactly probability is.

Probability can be defined as the measurement of a likelihood to occur . This is relatively straightforward, right? If you were to flip a coin, theres an equal mathematical probability - that is, an equal chance - that you will get 1) a heads, or 2) a tails.

In this manner, we can see that there are two outcomes . Outcomes are the end result of a single trial of a given experiment.

An experiment , then, is a situation involving probability. When you run an experiment, it will yield a certain outcome .

There are several different forms of experiments. They could range from something as simple as spinning a multi-colored spinner or flipping a coin, to something as complex as a lottery system. Because there are several different forms of experiments, there are also a great number of ways in which they could manifest.

They all, however, follow the same basic formula.

This formula will manifest in the following way, one hundred percent of the time:

probability = number of favorable outcomes / number of possible outcomes

So lets head back to the coin flip. Maybe you want it to land heads. Well, thats one favorable outcome. Now how many possible outcomes are there? Two, of course, because the coin obviously has two sides.

The calculation could then be done thusly:

probability ( p ) = number of favorable outcomes (1) / number of possible outcomes (2)

p = 1 / 2

p = 0.5

This shows us, then, that there is a 0.5 probability that well get a positive outcome, here being heads.

So now with the most elementary idea of this book out of the way, lets explore the bigger picture here. There are two massive concepts, tangentially related to probability and, indeed, derivative thereof: the ideas of permutations and combinations.

These concepts are very similar to one another, actually.

Before we jump into them, though, we need to jump into a simpler concept: a factorial . What a factorial is is a way of saying Hey, I want you to multiply n by itself minus 1, repeating all the way down to zero.

This may sound useless, but youll quickly see how it plays an important role as I explain permutations and combinations.

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