Brandon Royal - The Little Purple Probability Book: Mastering the Thinking Skills That Unlock the Secrets of Basic Probability

Copyright 2014 by Brandon Royal

1st Edition: This release, January 2014

All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical including photocopying, recording, or any information storage and retrieval system without permission in writing from the author or publisher.

Published by:

Maven Publishing
4520 Manilla Road
Calgary, Alberta, Canada T2G 4B7
www.mavenpublishing.com

Library and Archives Canada Cataloguing in Publication:

Royal, Brandon, author
The little purple probability book : mastering the thinking skills that unlock the secrets of basic probability / Brandon Royal

Issued in electronic and print formats.

ISBN 978-1-897393-67-3 (ebook)
ISBN 978-1-897393-65-9 (paperback)

1. Probabilities. 2. Probabilities--Problems, exercises, etc. I. Title.
QA273.R68 2014 519.2 C2012-905731-2

Technical Credits:
Cover Design: George Foster, Fairfield, Iowa, USA
Editing: Victory Crayne, Laguna, California, USA

Contents

INTRODUCTION

This guidebook is compiled with one primary goal in mind: To help readers master basic probability in the shortest possible time frame.

Achieving this goal requires two steps. The first step is to develop a superior conceptual framework for understanding probability. The overview section at the beginning of this material contains two strategic flowcharts one for probability and one for permutations and combinations the two main topics under review. Included is a summary of all 14 essential formulas, each accompanied by a relevant example. The second step is to practice on a small number of the most classic, thematic problems that represent the broader types of probability problems that may be found elsewhere.

Mastering the thinking skills to succeed in basic probability requires an ability to match a given problem with the correct formula. In order to properly categorize a problem, it is necessary to understand the often confusing terminology that surrounds probability and its related topics. For example, what does it mean to say that two events are independent or that they are not mutually exclusive? Once we are confident that we can sort problems into their common types, we can then judge whether a particular problem is a variation based on a classic problem type and/or whether it contains common traps that are otherwise easy to overlook. Special notes (marked "Note:") are imbedded throughout this material. Here the reader will find additional information, examples, or follow-up problems that will no doubt prove useful.

This guidebook provides a complement to The Little Green Math Book, which addresses basic but tricky math involving arithmetic and algebra. Probability is a subject that warrants special attention and this book serves as a stand-alone workshop.

Lets get started.

OVERVIEW

This material covers three main topics: probability, permutations, and combinations. What is the difference between probability and permutations and combinations? Probabilities are expressed as decimals or fractions between 0 and 1 (where 1 is the probability of certainty and 0 is the probability of impossibility) or, alternatively, as percentages between 0% and 100% (where 100% is the probability of certainty and 0% is the probability of impossibility). Permutations and combinations, on the other hand, result in outcomes greater than or equal to 1. Frequently they result in quite large outcomes such as 10, 36, 720, etc.

Probability:

In terms of probability, a quick rule of thumb is to determine first whether we are dealing with an and or or situation. And means multiply and or means addition. For example, if a problem states what is the probability of x and y, we multiply individual probabilities together. If a problem states what is the probability of x or y, we add individual probabilities together.

Moreover, if a probability problem requires us to multiply, we must ask one further question: Are the events independent or are the events dependent? Independent means that two events have no influence on one another and we simply multiply individual probabilities together to arrive at a final answer. Not independent (dependent) means that the occurrence of one event has an influence on the occurrence of another event and this influence must be taken into account.

Likewise, if a problem requires us to add probabilities, we must ask one further question: Are the events mutually exclusive or non-mutually exclusive? Mutually exclusive means that two events cannot occur at the same time and there is no overlap present. If two events have no overlap, we simply add probabilities. Not mutually exclusive means that two events can occur at the same time and that overlap is present. If two events do contain overlap, this overlap must not be double counted.

Permutations and Combinations:

With respect to permutations and combinations, permutations are ordered groups while combinations are unordered groups. Order matters in permutations; order does not matter in combinations. For example, AB and BA are considered different outcomes in permutations, but they are considered a single outcome in combinations. In real-life, examples of permutations include telephone numbers, license plates, electronic codes, and passwords. Examples of combinations include selection of members for a team or lottery tickets. In the case of lottery tickets, for instance, the order of numbers does not matter; we just need to get all the numbers, usually six of them.

As a practitioners rule, the words arrangements or possibilities imply permutations; the words select or choose imply combinations.

Factorials:

Factorial means that we engage multiplication such that:

Example: 4! = 4 3 2 1
Example: 7! = 7 6 5 4 3 2 1

Zero factorial equals one and one factorial also equals one:

Example: 0! = 1
Example: 1! = 1

Coins, Dice, Marbles, and Cards:

Problems in this guidebook include reference to coins, dice, marbles, and cards. For clarification purposes: The two sides of a coin are heads and tails. A die has six sides numbered from 1 to 6, with each having an equal likelihood of appearing subsequent to being tossed. The word die is singular; dice is plural. Marbles are assumed to be of a single, solid color. A deck of cards contains 52 cards divided equally into four suits clubs, diamonds, hearts, and spades where each suit contains 13 cards including ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, and 2.

Basic Probability Formulas

Here at a glance are the basic probability, permutation, and combination formulas used in this material.

Universal Formula

Example: You buy 3 raffle tickets and there are 10,000 tickets sold. What is the probability ofwinning the single prize?