| Introduction | p. 1 |
| The Nature of Probability | p. 5 |
| Probability and Everyday Speech | p. 5 |
| Spinning a Coin | p. 6 |
| Throwing or Spinning Other Objects | p. 8 |
| Problems 1 | p. 10 |
| Combining Probabilities | p. 13 |
| Either-or Probability | p. 13 |
| Both-and Probability | p. 15 |
| Genetically Inherited Disease - Just Gene Dependent | p. 16 |
| Genetically Dependent Disease - Gender Dependent | p. 19 |
| A Dice Game - American Craps | p. 21 |
| Problems 2 | p. 23 |
| A Day at the Races | p. 25 |
| Kinds of Probability | p. 25 |
| Betting on a Horse | p. 27 |
| The Best Conditions for a Punter | p. 31 |
| Problem 3 | p. 33 |
| Making Choices and Selections | p. 35 |
| Children Leaving a Room | p. 35 |
| Picking a Team | p. 37 |
| Choosing an Email Username | p. 40 |
| The UK National Lottery | p. 41 |
| Problems 4 | p. 44 |
| Non-Intuitive Examples of Probability | p. 45 |
| The Birthday Problem | p. 45 |
| Crown and Anchor | p. 49 |
| To Switch or Not to Switch - That is the Question | p. 52 |
| Problems 5 | p. 54 |
| Probability and Health | p. 55 |
| Finding the Best Treatment | p. 55 |
| Testing Drugs | p. 58 |
| Problems 6 | p. 64 |
| Combining Probabilities; The Craps Game Revealed | p. 67 |
| A Simple Probability Machine | p. 67 |
| Pontoon - A Card Game | p. 70 |
| The Throwers Chance of Winning at American Craps | p. 72 |
| Problems 7 | p. 75 |
| The UK National Lottery, Loaded Dice, and Crooked Wheels | p. 77 |
| The Need to Test for Fairness | p. 77 |
| Testing Random Numbers | p. 79 |
| The UK National Lottery | p. 82 |
| American Craps with Loaded Dice | p. 84 |
| Testing for a Loaded Die | p. 89 |
| The Roulette Wheel | p. 91 |
| Problems 8 | p. 93 |
| Block Diagrams | p. 95 |
| Variation in Almost Everything | p. 95 |
| A Shoe Manufacturer | p. 96 |
| Histogram Shapes | p. 99 |
| Lofty and Shorty | p. 101 |
| Problem 9 | p. 104 |
| The Normal (or Gaussian) Distribution | p. 105 |
| Probability Distributions | p. 105 |
| The Normal Distribution | p. 108 |
| The Variance and Standard Deviation | p. 110 |
| Properties of Normal Distributions | p. 111 |
| A Little Necessary Mathematics | p. 114 |
| Some Special Numbers | p. 114 |
| Powers of Numbers | p. 115 |
| The Form of the Normal Distribution | p. 117 |
| Random and Systematic Errors | p. 117 |
| Some Examples of the Normal Distribution | p. 119 |
| Electric Light Bulbs | p. 119 |
| People on Trolleys and Under-Used Resources | p. 120 |
| Problems 10 | p. 123 |
| Statistics - The Collection and Analysis of Numerical Data | p. 125 |
| Too Much Information | p. 125 |
| Another Way of Finding the Variance | p. 126 |
| From Regional to National Statistics | p. 127 |
| Problems 11 | p. 130 |
| The Poisson Distribution and Death by Horse Kicks | p. 131 |
| Rare Events | p. 131 |
| Typing a Manuscript | p. 133 |
| The Poisson Distribution as a Formula | p. 135 |
| Death by Horse Kicks | p. 137 |
| Some Other Examples of the Poisson Distribution | p. 139 |
| Flying Bomb Attacks on London | p. 139 |
| Clustering of a Disease | p. 141 |
| Some Further Examples | p. 142 |
| Problems 12 | p. 143 |
| Predicting Voting Patterns | p. 145 |
| Election Polls | p. 145 |
| Polling Statistics | p. 146 |
| Combining Polling Samples | p. 149 |
| Polling with More than Two Parties | p. 151 |
| Factors Affecting Polls and Voting | p. 153 |
| Problems 13 | p. 154 |
| Taking Samples - How Many Fish in the Pond? | p. 155 |
| Why do we Sample? | p. 155 |
| Finding out from Samples | p. 156 |
| An Illustrative Example | p. 158 |
| General Comments on Sampling | p. 160 |
| Quality Control | p. 160 |
| How Many Fish in the Pond? | p. 162 |
| Problems 14 | p. 164 |
| Differences - Rats and IQs | p. 165 |
| The Significance of Differences | p. 165 |
| Significantly Different - So What! | p. 167 |
| Problem 15 | p. 170 |
| Crime is Increasing and Decreasing | p. 171 |
| Crime and the Reporting of Crime | p. 171 |
| The Trend for Overall Crime in England and Wales | p. 172 |
| Vehicle Crime, Burglary, and Violent Crime | p. 174 |
| Homicide | p. 177 |
| Crime and Politicians | p. 179 |
| Problem 16 | p. 181 |
| My Uncle Joe Smoked 60 a Day | p. 183 |
| Genetics and Disease | p. 183 |
| The Incidence of Smoking in the United Kingdom | p. 185 |
| The Smoking Lottery | p. 187 |
| Problem 17 | p. 189 |
| Chance, Luck, and Making Decisions | p. 191 |
| The Winds of Chance | p. 191 |
| Choices | p. 194 |
| I Want a Lucky General | p. 195 |
| To Fight or Not to Fight - That is the Question | p. 197 |
| The Mathematics of War | p. 200 |
| Problem 18 | p. 204 |
| Solutions to Problems | p. 205 |
| Index | p. 221 |
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