Everyday Probability and Statistics: Health, Elections, Gambling and War Book

Introduction 1

Chapter 1 The Nature of Probability 7

1.1 Probability and Everyday Speech 7

1.2 Spinning a Coin 8

1.3 Throwing or Spinning Other Objects 10

Problems 1 12

Chapter 2 Combining Probabilities 15

2.1 Either-or Probability 15

2.2 Both-and Probability 17

2.3 Genetically Inherited Disease ? Just Gene Dependent 18

2.4 Genetically Inherited Disease ? Gender Dependent 21

2.5 A Dice Game - American Craps 23

Problems 2 25

Chapter 3 A Day at the Races 27

3.1 Kinds of Probability 27

3.2 Betting on a Horse 29

3.3 The Best Conditions for a Punter 33

Problem 3 35

Chapter 4 Making Choices and Selections 37

4.1 Children Leaving a Room 37

4.2 Picking a Team 39

4.3 Choosing an Email Username 42

4.4 The UK National Lottery 43

Problems 4 47

Chapter 5 Non-Intuitive Examples of Probability 49

5.1 The Birthday Problem 49

5.2 Crown and Anchor 53

5.3 To Switch or Not to Switch, That is the Question 56

Problems 5 58

Chapter 6 Probability and Health 59

6.1 Finding the Best Treatment. 59

6.2 Testing Drugs 62

Problems 6 68

Chapter 7 Combining Probabilities: The Craps Game Revealed 71

7.1 A Simple Probability Machine 71

7.2 Pontoon: A Card Game 74

7.3 The Thrower's Chance of Winning at American Craps 76

Problems 7 79

Chapter 8 The UK National Lottery, Loaded Dice and Crooked Wheels 81

8.1 The Need to Test for Fairness 81

8.2 Testing Random Numbers 83

8.3 The UK National Lottery 87

8.4 American Craps with Loaded Dice 89

8.5 Testing for a Loaded Die 94

8.6 The Roulette Wheel 96

Problems 8 98

Chapter 9 Block Diagrams 101

9.1 Variation in Almost Everything 101

9.2 A Shoe Manufacturer 102

9.3 Histogram Shapes 105

9.4 Lofty and Shorty 107

Problem 9 110

Chapter 10 The Normal (or Gaussian) Distribution 111

10.1 Probability Distributions 111

10.2 The Normal Distribution 113

10.3 The Variance and Standard Deviation 115

10.4 Properties of Normal Distributions 117

10.5 A Little Necessary Mathematics 119

10.5.1 Some special numbers 119

10.5.2 Powers of numbers 120

10.6 The Form of the Normal Distribution 122

10.7 Random and Systematic Errors 123

10.8 Some Examples of the Normal Distribution 125

10.8.1 Electric light bulbs 125

10.8.2 People on trolleys and under-used resources 126

Problems 10 128

Chapter 11 Statistics: The Collection and Analysis of Numerical Data 129

11.1 Too Much Information 129

11.2 Another Way of Finding the Variance 130

11.3 From Regional to National Statistics 131

Problems 11 133

Chapter 12 The Poisson Distribution and Death by Horse Kicks 135

12.1 Rare Events 135

12.2 Typing a Manuscript 137

12.3 The Poisson Distribution as a Formula 139

12.4 Death by Horse Kicks 141

12.5 Some Other Examples of the Poisson Distribution 143

12.5.1 Flying Bomb Attacks on London 143

12.5.2 Clustering of a disease 145

12.5.3 Some further examples 146

Problems 12 147

Chapter 13 Predicting Voting Patterns 149

13.1 Election Polls 149

13.2 Polling Statistics 150

13.3 Combining Polling Samples 153

13.4 Polling with More than Two Parries 154

13.5 Factors Affecting Polls and Voting 156

Problems 13 158

Chapter 14 Taking Samples: How Many Fish in the Pond? 159

14.1 Why Do We Sample? 159

14.2 Finding Out From Samples 160

14.3 An Illustrative Example 162

14.4 General Comments on Sampling 164

14.5 Quality Control 164

14.6 How Many Fish in the Pond? 167

Problems 14 168

Chapter 15 Differences: Rats and IQs 171

15.1 The Significance of Differences 171

15.2 Significantly Different -So What! 173

Problem 15 176

Chapter 16 Crime is Increasing and Decreasing 177

16.1 Crime and the Reporting of Crime 177

16.2 The Trend for Overall Crime in England and Wales 178

16.3 Vehicle Crime, Burglary and Violent Crime 180

16.4 Homicide 183

16.5 Crime and Politicians 185

Problem 16 186

Chapter 17 My Uncle Joe Smoked 60 a Day 189

17.1 Genetics and Disease 189

17.2 The Incidence of Smoking in the UK 191

17.3 The Smoking Lottery 193

Problem 17 195

Chapter 18 Chance, Luck and Making Decisions 197

18.1 The Winds of Chance 197

18.2 Choices 200

18.3 I Want a Lucky General 201

18.4 To Fight or Not to Fight, That is the Question 203

18.5 The Mathematics of War 206

Problem 18 210

Chapter 19 Science and Society 211

19.1 What is Science? 212

19.2 Meteorology and Butterflies 214

9.2.1 A demonstration of chaos 215

9.2.2 Meteorological forecasting 218

19.3 Global Warming 223

19.3.1 The greenhouse effect 224

19.3.2 Greenhouse gases 228

19.3.3 The evidence for global warming 229

19.3.4 The controversy 232

19.3.5 Can we know for certain? 233

19.3.6 Better safe than sorry 237

19.4 Nuclear Power Generation 239

19.5 Decision-Making Without Hard Data 242

Problem 19 244

Chapter 20 The Pensions Problem 245

20.1 A History of Life Expectancy 245

20.2 Supporting the Aged, and Others 249

20.3 The Age Structure of Populations 252

20.4 The Arithmetic of Pensions 254

Problem 20 258

Solutions to Problems 259

Index 275