| Introduction | p. 1 |
| The Nature of Probability | p. 7 |
| Probability and Everyday Speech | p. 7 |
| Spinning a Coin | p. 8 |
| Throwing or Spinning Other Objects | p. 10 |
| Problems 1 | p. 12 |
| Combining Probabilities | p. 15 |
| Either-or Probability | p. 15 |
| Both-and Probability | p. 17 |
| Genetically Inherited Disease - Just Gene Dependent | p. 18 |
| Genetically Inherited Disease - Gender Dependent | p. 21 |
| A Dice Game - American Craps | p. 23 |
| Problems 2 | p. 25 |
| A Day at the Races | p. 27 |
| Kinds of Probability | p. 27 |
| Betting on a Horse | p. 29 |
| The Best Conditions for a Punter | p. 33 |
| Problem 3 | p. 35 |
| Making Choices and Selections | p. 37 |
| Children Leaving a Room | p. 37 |
| Picking a Team | p. 39 |
| Choosing an Email Username | p. 42 |
| The UK National Lottery | p. 43 |
| Problems 4 | p. 47 |
| Non-Intuitive Examples of Probability | p. 49 |
| The Birthday Problem | p. 49 |
| Crown and Anchor | p. 53 |
| To Switch or not to Switch, that is the Question | p. 56 |
| Problems 5 | p. 58 |
| Probability and Health | p. 59 |
| Finding the Best Treatment | p. 59 |
| Testing Drugs | p. 62 |
| Problems 6 | p. 68 |
| Combining Probabilities: The Craps Game Revealed | p. 71 |
| A Simple Probability Machine | p. 71 |
| Pontoon: A Card Game | p. 74 |
| The Thrower's Chance of Winning at American Craps | p. 76 |
| Problems 7 | p. 79 |
| The UK National Lottery, Loaded Dice and Crooked Wheels | p. 81 |
| The Need to Test for Fairness | p. 81 |
| Testing Random Numbers | p. 83 |
| The UK National Lottery | p. 87 |
| American Craps with Loaded Dice | p. 89 |
| Testing for a Loaded Die | p. 94 |
| The Roulette Wheel | p. 96 |
| Problems 8 | p. 98 |
| Block Diagrams | p. 101 |
| Variation in Almost Everything | p. 101 |
| A Shoe Manufacturer | p. 102 |
| Histogram Shapes | p. 105 |
| Lofty and Shorty | p. 107 |
| Problem 9 | p. 110 |
| The Normal (or Gaussian) Distribution | p. 111 |
| Probability Distributions | p. 111 |
| The Normal Distribution | p. 113 |
| The Variance and Standard Deviation | p. 115 |
| Properties of Normal Distributions | p. 117 |
| A Little Necessary Mathematics | p. 119 |
| Some special numbers | p. 119 |
| Powers of numbers | p. 120 |
| The Form of the Normal Distribution | p. 122 |
| Random and Systematic Errors | p. 123 |
| Some Examples of the Normal Distribution | p. 125 |
| Electric light bulbs | p. 125 |
| People on trolleys and under-used resources | p. 126 |
| Problems 10 | p. 128 |
| Statistics: The Collection and Analysis of Numerical Data | p. 129 |
| Too Much Information | p. 129 |
| Another Way of Finding the Variance | p. 130 |
| From Regional to National Statistics | p. 131 |
| Problems 11 | p. 133 |
| The Poisson Distribution and Death by Horse Kicks | p. 135 |
| Rare Events | p. 135 |
| Typing a Manuscript | p. 137 |
| The Poisson Distribution as a Formula | p. 139 |
| Death by Horse Kicks | p. 141 |
| Some Other Examples of the Poisson Distribution | p. 143 |
| Flying Bomb Attacks on London | p. 143 |
| Clustering of a disease | p. 145 |
| Some further examples | p. 146 |
| Problems 12 | p. 147 |
| Predicting Voting Patterns | p. 149 |
| Election Polls | p. 149 |
| Polling Statistics | p. 150 |
| Combining Polling Samples | p. 153 |
| Polling with More than Two Parties | p. 154 |
| Factors Affecting Polls and Voting | p. 156 |
| Problems 13 | p. 158 |
| Taking Samples: How Many Fish in the Pond? | p. 159 |
| Why Do we Sample? | p. 159 |
| Finding out from Samples | p. 160 |
| An Illustrative Example | p. 162 |
| General Comments on Sampling | p. 164 |
| Quality Control | p. 164 |
| How Many Fish in the Pond? | p. 167 |
| Problems 14 | p. 168 |
| Differences: Rats and IQs | p. 171 |
| The Significance of Differences | p. 171 |
| Significantly Different - So What! | p. 173 |
| Problem 15 | p. 176 |
| Crime is Increasing and Decreasing | p. 177 |
| Crime and the Reporting of Crime | p. 177 |
| The Trend for Overall Crime in England and Wales | p. 178 |
| Vehicle Crime, Burglary and Violent Crime | p. 180 |
| Homicide | p. 183 |
| Crime and Politicians | p. 185 |
| Problem 16 | p. 186 |
| My Uncle Joe Smoked 60 a Day | p. 189 |
| Genetics and Disease | p. 189 |
| The Incidence of Smoking in the UK | p. 191 |
| The Smoking Lottery | p. 193 |
| Problem 17 | p. 195 |
| Chance, Luck and Making Decisions | p. 197 |
| The Winds of Chance | p. 197 |
| Choices | p. 200 |
| I Want a Lucky General | p. 201 |
| To Fight or not to Fight, that is the Question | p. 203 |
| The Mathematics of War | p. 206 |
| Problem 18 | p. 210 |
| Science and Society | p. 211 |
| What is Science? | p. 212 |
| Meteorology and Butterflies | p. 214 |
| A demonstration of chaos | p. 215 |
| Meteorological forecasting | p. 218 |
| Global Warming | p. 223 |
| The greenhouse effect | p. 224 |
| Greenhouse gases | p. 228 |
| The evidence for global warming | p. 229 |
| The controversy | p. 232 |
| Can we know for certain? | p. 233 |
| Better safe than sorry | p. 237 |
| Nuclear Power Generation | p. 239 |
| Decision-Making without Hard Data | p. 242 |
| Problem 19 | p. 244 |
| The Pensions Problem | p. 245 |
| A History of Life Expectancy | p. 245 |
| Supporting the Aged, and Others | p. 249 |
| The Age Structure of Populations | p. 252 |
| The Arithmetic of Pensions | p. 254 |
| Problem 20 | p. 258 |
| Solutions to Problems | p. 259 |
| Index | p. 275 |
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