Beginner’s Guide to Probability: Now’s Your Chance!

Beginner’s Guide to Probability: now’s your chance!

Duncan Williamson

excelmaster.co

February 2016

Contents

Beginner’s Guide to Probability: now’s your chance!

Introduction

Probability in Real Life

The Car Insurance Problem

Roll the Dice

Let’s Win the Lottery … Not

Want to play a game where you’ve got a much better chance of winning?

The Probability of Contacting other Civilisations

An Overview with Some Excellent Examples from History

Objective and Subjective Probabilities

All Roads Probably Lead to 1

At Random

Exercise 1

Exercise 1 Solution

Probability of Success

Exercise 2

Exercise 2 Solution

Put it all Together now: exercises to confirm the basics

Exercise 3

Exercise 3 Solution

Exercise 4

Exercise 4 Solution

Exercise 5

Exercise 5 Solution

Exercise 6

Exercise 6 Solution

Exercise 7

Exercise 7 Solution

Deduction: elementary my dear Watson!

Thanks for the Complement, Holmes

Example 8

Example 8 Solution

Example 9

Example 9 Solution

Example 10

Example 10 Solution

Mutually Exclusive Events

Example 11

Example 11 Solution

Probabilities and Frequencies

Example 12

Example 12 Solution

Relative Frequency Diagrams

Possibility Spaces

Example 13

Example 13 Solution

Example 14

Example 14 Solution

Tree Diagrams

Example 15

Example 15 Solution

Using the Tree Diagrams: independent events

Example 16

Example 16 Solution

Example 17

Example 17 Solution

Sorting out Hideous Outcomes: use plain language

Example 18

Example 18 Solution

Example 19

Example 19 Solution

Binomial Probabilities

Characteristics of a Binomial Random Variable

Example 20

Example 20 Solution

Example 21

Example 21 Solution

Example 22

Example 22 Solution

Predicting each Event: combinations

Binomial Probability Tables

Binomial Probability Table Examples

Working Without the Binomial Probability Tables

Example 23

Example 23 Solution

Example 24 do

Example 24 Solution

Excel, the Formula and Cumulative Results

Conclusions

References

Appendix Mathematical Notation

The Probability Scale

The Complementary Event Ec

The Addition Rule: mutually exclusive events

Exhaustive Events

The Multiplication Rule

Combinations Formula

Conditional Probability

Statistical Independence

The Cumulative Probability Distribution Function

The Discrete Uniform Distribution

The Geometric Distribution

Cumulative Probabilities

Beginner’s Guide to Probability: now’s your chance!

This book should be of interest to anyone beginning their study of probability analysis. Based on mathematical examples, it will satisfy students working towards a variety of examinations that includes GCSE Mathematics, A Level Mathematics, Professional Accountancy examinations at level 1, Undergraduate Accountancy and Business courses.

In terms of academic and professional education and training, probability is taught and examined in a very wide variety of settings and at a wide variety of levels. for example, we can find probability at GCSE level (16 year school exit exams) and we can find them