4. A Curious Coin-Flipping Game

Kapitel in diesem Buch

1. Frontmatter i
2. Contents ix
3. Preface to the Paperback Edition xiii
4. ntroduction 1
5. The Problems
6. 1. The Clumsy Dishwasher Problem 37
7. 2. Will Lil and Bill Meet at the Malt Shop? 38
8. 3. A Parallel Parking Question 40
9. 4. A Curious Coin-Flipping Game 42
10. 5. The Gamow-Stern Elevator Puzzle 45
11. 6. Steve’s Elevator Problem 48
12. 7. The Pipe Smoker’s Discovery 51
13. 8. A Toilet Paper Dilemma 53
14. 9. The Forgetful Burglar Problem 59
15. 10. The Umbrella Quandary 61
16. 11. The Case of the Missing Senators 63
17. 12. How Many Runners in a Marathon? 65
18. 13. A Police Patrol Problem 69
19. 14. Parrondo’s Paradox 74
20. 15. How Long Is the Wait to Get the Potato Salad? 77
21. 16. The Appeals Court Paradox 81
22. 17. Waiting for Buses 83
23. 18. Waiting for Stoplights 85
24. 19. Electing Emperors and Popes 87
25. 20. An Optimal Stopping Problem 91
26. 21. Chain Reactions, Branching Processes, and Baby Boys 96
27. The Solutions
28. 1. The Clumsy Dishwasher Problem 103
29. 2. Will Lil and Bill Meet at the Malt Shop? 105
30. 3. A Parallel Parking Question 109
31. 4. A Curious Coin-Flipping Game 114
32. 5. The Gamow-Stern Elevator Puzzle 120
33. 6. Steve’s Elevator Problem 124
34. 7. The Pipe Smoker’s Discovery 129
35. 8. A Toilet Paper Dilemma 140
36. 9. The Forgetful Burglar Problem 144
37. 10. The Umbrella Quandary 148
38. 11. The Case of the Missing Senators 153
39. 12. How Many Runners in a Marathon? 157
40. 13. A Police Patrol Problem 161
41. 14. Parrondo’s Paradox 169
42. 15. How Long Is theWait to Get the Potato Salad? 175
43. 16. The Appeals Court Paradox 184
44. 17. Waiting for Buses 187
45. 18. Waiting for Stoplights 191
46. 19. Electing Emperors and Popes 197
47. 20. An Optimal Stopping Problem 204
48. 21. Chain Reactions, Branching Processes, and Baby Boys 213
49. Appendix 1. One Way to Guess on a Test 221
50. Appendix 2. An Example of Variance Reduction in the Monte Carlo Method 223
51. Appendix 3. Random Harmonic Series 229
52. Appendix 4. Solving Montmort’s Problem by Recursion 231
53. Appendix 5. An Illustration of the Inclusion-Exclusion Principle 237
54. Appendix 6. Solutions to the Spin Game 244
55. Appendix 7. How to Simulate Kelvin’s Fair Coin with a Biased Coin 248
56. Appendix 8. How to Simulate an Exponential Random Variable 252
57. Appendix 9. Author-Created MATLAB m-files and Their Location in the Book 255
58. Glossary 257
59. Acknowledgments 259
60. Index 261
61. Also by Paul J. Nahin 265