MATH PROBABILITY Book Every Day Life 4 Aaaaa
of 5
Transcript of MATH PROBABILITY Book Every Day Life 4 Aaaaa
-
7/30/2019 MATH PROBABILITY Book Every Day Life 4 Aaaaa
1/5
EVERYDAY PROBABILITY AND STATISTICS - Health, Elections, Gambling and War
Imperial College Press
http://www.worldscibooks.com/mathematics/p543.html
Contents
Introduction 1
Chapter 1 The Nature of Probability 5
1.1. Probability and Everyday Speech . . . . . . . . . . . . 5
1.2. Spinning a Coin . . . . . . . . . . . . . . . . . . . . . . 6
1.3. Throwing or Spinning Other Objects . . . . . . . . . . 8
Problems 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Chapter 2 Combining Probabilities 13
2.1. Eitheror Probability . . . . . . . . . . . . . . . . . . . 13
2.2. Bothand Probability . . . . . . . . . . . . . . . . . . . 15
2.3. Genetically Inherited Disease Just Gene Dependent 16
2.4. Genetically Dependent Disease Gender Dependent 19
2.5. A Dice Game American Craps . . . . . . . . . . . . 21Problems 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 3 A Day at the Races 25
3.1. Kinds of Probability . . . . . . . . . . . . . . . . . . . . 25
3.2. Betting on a Horse . . . . . . . . . . . . . . . . . . . . . 27
3.3. The Best Conditions for a Punter . . . . . . . . . . . . 31
Problem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Chapter 4 Making Choices and Selections 35
4.1. Children Leaving a Room . . . . . . . . . . . . . . . . 35
v
-
7/30/2019 MATH PROBABILITY Book Every Day Life 4 Aaaaa
2/5
EVERYDAY PROBABILITY AND STATISTICS - Health, Elections, Gambling and War
Imperial College Press
http://www.worldscibooks.com/mathematics/p543.html
vi Everyday Probability and Statistics
4.2. Picking a Team . . . . . . . . . . . . . . . . . . . . . . . 37
4.3. Choosing an Email Username . . . . . . . . . . . . . . 40
4.4. The UK National Lottery . . . . . . . . . . . . . . . . . 41Problems 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 5 Non-Intuitive Examples of Probability 45
5.1. The Birthday Problem . . . . . . . . . . . . . . . . . . 45
5.2. Crown and Anchor . . . . . . . . . . . . . . . . . . . . 49
5.3. To Switch or Not to Switch That is the Question . . 52
Problems 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Chapter 6 Probability and Health 55
6.1. Finding the Best Treatment . . . . . . . . . . . . . . . . 55
6.2. Testing Drugs . . . . . . . . . . . . . . . . . . . . . . . 58
Problems 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Chapter 7 Combining Probabilities; The CrapsGame Revealed 67
7.1. A Simple Probability Machine . . . . . . . . . . . . . . 67
7.2. Pontoon A Card Game . . . . . . . . . . . . . . . . . 70
7.3. The Throwers Chance of Winning at American Craps 72
Problems 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Chapter 8 The UK National Lottery, Loaded Dice,and Crooked Wheels 77
8.1. The Need to Test for Fairness . . . . . . . . . . . . . . 77
8.2. Testing Random Numbers . . . . . . . . . . . . . . . . 79
8.3. The UK National Lottery . . . . . . . . . . . . . . . . . 82
8.4. American Craps with Loaded Dice . . . . . . . . . . . 84
8.5. Testing for a Loaded Die . . . . . . . . . . . . . . . . . 89
8.6. The Roulette Wheel . . . . . . . . . . . . . . . . . . . . 91
Problems 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
-
7/30/2019 MATH PROBABILITY Book Every Day Life 4 Aaaaa
3/5
EVERYDAY PROBABILITY AND STATISTICS - Health, Elections, Gambling and War
Imperial College Press
http://www.worldscibooks.com/mathematics/p543.html
Contents vii
Chapter 9 Block Diagrams 95
9.1. Variation in Almost Everything . . . . . . . . . . . . . 95
9.2. A Shoe Manufacturer . . . . . . . . . . . . . . . . . . . 969.3. Histogram Shapes . . . . . . . . . . . . . . . . . . . . . 99
9.4. Lofty and Shorty . . . . . . . . . . . . . . . . . . . . . . 101
Problem 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Chapter 10 The Normal (or Gaussian) Distribution 105
10.1. Probability Distributions . . . . . . . . . . . . . . . . . 105
10.2. The Normal Distribution . . . . . . . . . . . . . . . . . 108
10.3. The Variance and Standard Deviation . . . . . . . . . 110
10.4. Properties of Normal Distributions . . . . . . . . . . . 111
10.5. A Little Necessary Mathematics . . . . . . . . . . . . . 114
10.5.1. Some Special Numbers . . . . . . . . . . . . . . 114
10.5.2. Powers of Numbers . . . . . . . . . . . . . . . . 115
10.6. The Form of the Normal Distribution . . . . . . . . . . 117
10.7. Random and Systematic Errors . . . . . . . . . . . . . 117
10.8. Some Examples of the Normal Distribution . . . . . . 119
10.8.1. Electric Light Bulbs . . . . . . . . . . . . . . . . 119
10.8.2. People on Trolleys and Under-Used Resources 120
Problems 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Chapter 11 Statistics The Collection and Analysis
of Numerical Data 125
11.1. Too Much Information . . . . . . . . . . . . . . . . . . 125
11.2. Another Way of Finding the Variance . . . . . . . . . . 126
11.3. From Regional to National Statistics . . . . . . . . . . 127
Problems 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Chapter 12 The Poisson Distribution and Deathby Horse Kicks 131
12.1. Rare Events . . . . . . . . . . . . . . . . . . . . . . . . 131
12.2. Typing a Manuscript . . . . . . . . . . . . . . . . . . . 133
-
7/30/2019 MATH PROBABILITY Book Every Day Life 4 Aaaaa
4/5
EVERYDAY PROBABILITY AND STATISTICS - Health, Elections, Gambling and War
Imperial College Press
http://www.worldscibooks.com/mathematics/p543.html
viii Everyday Probability and Statistics
12.3. The Poisson Distribution as a Formula . . . . . . . . . 135
12.4. Death by Horse Kicks . . . . . . . . . . . . . . . . . . . 137
12.5. Some Other Examples of the Poisson Distribution . . 13912.5.1. Flying Bomb Attacks on London . . . . . . . . 139
12.5.2. Clustering of a Disease . . . . . . . . . . . . . . 141
12.5.3. Some Further Examples . . . . . . . . . . . . . 142
Problems 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Chapter 13 Predicting Voting Patterns 145
13.1. Election Polls . . . . . . . . . . . . . . . . . . . . . . . . 14513.2. Polling Statistics . . . . . . . . . . . . . . . . . . . . . . 146
13.3. Combining Polling Samples . . . . . . . . . . . . . . . 149
13.4. Polling with More than Two Parties . . . . . . . . . . . 151
13.5. Factors Affecting Polls and Voting . . . . . . . . . . . 153
Problems 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Chapter 14 Taking Samples How Many Fish in the Pond? 15514.1. Why do we Sample? . . . . . . . . . . . . . . . . . . . 155
14.2. Finding out from Samples . . . . . . . . . . . . . . . . 156
14.3. An Illustrative Example . . . . . . . . . . . . . . . . . 158
14.4. General Comments on Sampling . . . . . . . . . . . . 160
14.5. Quality Control . . . . . . . . . . . . . . . . . . . . . . 160
14.6. How Many Fish in the Pond? . . . . . . . . . . . . . . 162
Problems 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Chapter 15 Differences Rats and IQs 165
15.1. The Significance of Differences . . . . . . . . . . . . . 165
15.2. Significantly Different So What! . . . . . . . . . . . 167
Problem 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Chapter 16 Crime is Increasing and Decreasing 171
16.1. Crime and the Reporting of Crime . . . . . . . . . . . 171
16.2. The Trend for Overall Crime in England and Wales . . 172
16.3. Vehicle Crime, Burglary, and Violent Crime . . . . . . 174
-
7/30/2019 MATH PROBABILITY Book Every Day Life 4 Aaaaa
5/5
EVERYDAY PROBABILITY AND STATISTICS - Health, Elections, Gambling and War
Imperial College Press
http://www.worldscibooks.com/mathematics/p543.html
Contents ix
16.4. Homicide . . . . . . . . . . . . . . . . . . . . . . . . . . 177
16.5. Crime and Politicians . . . . . . . . . . . . . . . . . . . 179
Problem 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Chapter 17 My Uncle Joe Smoked 60 a Day 183
17.1. Genetics and Disease . . . . . . . . . . . . . . . . . . . 183
17.2. The Incidence of Smoking in the United Kingdom . . 185
17.3. The Smoking Lottery . . . . . . . . . . . . . . . . . . . 187
Problem 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Chapter 18 Chance, Luck, and Making Decisions 191
18.1. The Winds of Chance . . . . . . . . . . . . . . . . . . . 191
18.2. Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
18.3. I Want a Lucky General . . . . . . . . . . . . . . . . . . 195
18.4. To Fight or Not to Fight That is the Question . . . . 197
18.5. The Mathematics of War . . . . . . . . . . . . . . . . . 200
Problem 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Solutions to Problems 205
Index 221
