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Will You Be Alive 10 Years from Now?

Book Description

What are the chances of a game-show contestant finding a chicken in a box? Is the Hanukkah dreidel a fair game? Will you be alive ten years from now? These are just some of the one-of-a-kind probability puzzles that acclaimed popular math writer Paul Nahin offers in this lively and informative book.

Nahin brings probability to life with colorful and amusing historical anecdotes as well as an electrifying approach to solving puzzles that illustrates many of the techniques that mathematicians and scientists use to grapple with probability. He looks at classic puzzles from the past--from Galileo's dice-tossing problem to a disarming dice puzzle that would have astonished even Newton--and also includes a dozen challenge problems for you to tackle yourself, with complete solutions provided in the back of the book.

Nahin then presents twenty-five unusual probability puzzlers that you aren't likely to find anywhere else, and which range in difficulty from ones that are easy but clever to others that are technically intricate. Each problem is accompanied by an entertaining discussion of its background and solution, and is backed up by theory and computer simulations whenever possible in order to show how theory and computer experimentation can often work together on probability questions. All the MATLAB® Monte Carlo simulation codes needed to solve the problems computationally are included in the book.With his characteristic wit, audacity, and insight, Nahin demonstrates why seemingly simple probability problems can stump even the experts.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Dedication Page
  5. Contents
  6. Preface
  7. Introduction: Classic Puzzles from the Past
    1. I.1 A Gambling Puzzle of Gombaud and Pascal
    2. I.2 Galileo’s Dice Problem
    3. I.3 Another Gombaud-Pascal Puzzle
    4. I.4 Gambler’s Ruin and De Moivre
    5. I.5 Monte Carlo Simulation of Gambler’s Ruin
    6. I.6 Newton’s Probability Problem
    7. I.7 A Dice Problem That Would Have Surprised Newton
    8. I.8 A Coin-Flipping Problem
    9. I.9 Simpson’s Paradox, Radio-Direction Finding, and the Spaghetti Problem
  8. Challenge Problems
  9. 1 Breaking Sticks
    1. 1.1 The Problem
    2. 1.2 Theoretical Analysis
    3. 1.3 Computer Simulation
  10. 2 The Twins
    1. 2.1 The Problem
    2. 2.2 Theoretical Analysis
    3. 2.3 Computer Simulation
  11. 3 Steve’s Elevator Problem
    1. 3.1 The Problem
    2. 3.2 Theoretical Analysis by Shane Henderson
    3. 3.3 Computer Simulation
  12. 4 Three Gambling Problems Newton Would “Probably” Have Liked
    1. 4.1 The Problems
    2. 4.2 Theoretical Analysis 1
    3. 4.3 Computer Simulation 1
    4. 4.4 Theoretical Analysis 2
    5. 4.5 Computer Simulation 2
    6. 4.6 Theoretical Analysis 3
  13. 5 Big Quotients—Part 1
    1. 5.1 The Problem
    2. 5.2 Theoretical Analysis
    3. 5.3 Computer Simulation
  14. 6 Two Ways to Proofread
    1. 6.1 The Problem
    2. 6.2 Theoretical Analysis
  15. 7 Chain Letters That Never End
    1. 7.1 The Problem
    2. 7.2 Theoretical Analysis
  16. 8 Bingo Befuddlement
    1. 8.1 The Problem
    2. 8.2 Computer Simulation
  17. 9 Is Dreidel Fair?
    1. 9.1 The Problem
    2. 9.2 Computer Simulation
  18. 10 Hollywood Thrills
    1. 10.1 The Problem
    2. 10.2 Theoretical Analysis
  19. 11 The Problem of the n-Liars
    1. 11.1 The Problem
    2. 11.2 Theoretical Analysis
    3. 11.3 Computer Simulation
  20. 12 The Inconvenience of a Law
    1. 12.1 The Problem
    2. 12.2 Theoretical Analysis
  21. 13 A Puzzle for When the Super Bowl is a Blowout
    1. 13.1 The Problem
    2. 13.2 Theoretical Analysis
  22. 14 Darts and Ballistic Missiles
    1. 14.1 The Problem
    2. 14.2 Theoretical Analysis
  23. 15 Blood Testing
    1. 15.1 The Problem
    2. 15.2 Theoretical Analysis
  24. 16 Big Quotients—Part 2
    1. 16.1 The Problem
    2. 16.2 Theoretical Analysis
  25. 17 To Test or Not to Test?
    1. 17.1 The Problem
    2. 17.2 Theoretical Analysis
  26. 18 Average Distances on a Square
    1. 18.1 The Problem(s)
    2. 18.2 Theoretical Analyses
    3. 18.3 Computer Simulations
  27. 19 When Will the Last One Fail?
    1. 19.1 The Problem
    2. 19.2 Theoretical Analyses
  28. 20 Who’s Ahead?
    1. 20.1 The Problem
    2. 20.2 Theoretical Analysis
  29. 21 Plum Pudding
    1. 21.1 The Problem
    2. 21.2 Computer Simulation
    3. 21.3 Theoretical Analysis
  30. 22 Ping-Pong, Squash, and Difference Equations
    1. 22.1 Ping-Pong Math
    2. 22.2 Squash Math Is Harder!
  31. 23 Will You Be Alive 10 Years from Now?
    1. 23.1 The Problem
    2. 23.2 Theoretical Analysis
  32. 24 Chickens in Boxes
    1. 24.1 The Problem (and Some Warm-ups, Too)
    2. 24.2 Theoretical Analysis
  33. 25 Newcomb’s Paradox
    1. 25.1 Some History
    2. 25.2 Decision Principles in Conflict
  34. Challenge Problem Solutions
  35. Technical Note on MATLAB®’s Random Number Generator
  36. Acknowledgments
  37. Index