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Fifty Challenging Problems in Probability


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Table of Contents

1. The sock drawer 2. Successive wins 3. The flippant juror 4. Trials until first success 5. Coin in square 6. Chuck-a-luck 7. Curing the compulsive gambler 8. Perfect bridge hand 9. Craps 10. An experiment in personal taste for money 11. Silent cooperation 12. Quo vadis? 13. The prisoner's dilemma 14. "Collecting coupons, including Euler's approximation for harmonic sums" 15. The theater row 16. Will second-best be runner-up? 17. Twin knights 18. "An even split at coin tossing, including Stirling's approximation" 19. Isaac Newton helps Samuel Pepys 20. The three-cornered duel 21. Should you sample with or without replacement? 22. The ballot box 23. Ties in matching pennies 24. The unfair subway 25. Lengths of random chords 26. The hurried duelers 27. Catching the cautious counterfeiter 28. "Catching the greedy counterfeiter, including the Poisson distribution" 29. Moldy gelation 30. Evening the sales 31. Birthday pairings 32. Finding your birthmate 33. Relating the birthday pairings and birthmate problems 34. Birthday holidays 35. The cliff-hanger 36. Gambler's ruin 37. Bold play vs. cautious play 38. The thick coin Digression: A note on the principle of symmetry when points are dropped on a line 39. The clumsy chemist 40. The first ace 41. The locomotive problem 42. The little end of the stick 43. The broken bar 44. Winning an unfair game 45. Average number of matches 46. Probabilities of matches 47. Choosing the largest dowry 48. Choosing the largest random number 49. Doubling your accuracy 50. Random quadratic equations 51. Two-dimensional random walk 52. Three-dimensional random walk 53. Buffon's needle 54. Buffon's needle with horizontal and vertical rulings 55. Long needles 56. Molina's urns

About the Author

Charles Frederick Mosteller ( 1916-2006) was one of the eminent statisticians of the 20th century. He was the founding chairman of Harvard's Statistics department. Dr. Mosteller wrote more than 50 books and more than 350 papers, with over 200 coauthors. Frederick Mosteller: Harvard Man Frederick Mosteller (1916-2006) founded Harvard University's Department of Statistics and served as its first chairman from 1957 until 1969 and again for several years in the 1970s. He was the author or co-author of more than 350 scholarly papers and more than 50 books, including one of the most popular books in his field, first published in 1965 and reprinted by Dover in 1987, Fifty Challenging Problems in Probability with Solutions. Mosteller's work was wide-ranging: He used statistical analysis of written works to prove that James Madison was the author of several of the Federalist papers whose authorship was in dispute. With then-Harvard professor and later Senator Daniel P. Moynihan, he studied what would be the most effective way of helping students from impoverished families do better in school - their answer: to improve income levels rather than to simply spend on schools. Later, his analysis of the importance to learning of smaller class sizes buttressed the Clinton Administration's initiative to hire 100,000 teachers. And, as far back as the 1940s, Mosteller composed an early statistical analysis of baseball: After his team, the Boston Red Sox, lost the 1946 World Series, he demonstrated that luck plays an enhanced role in a short series, even for a strong team. In the Author's Own Words: "Though we often hear that data can speak for themselves, their voices can be soft and sly." - Frederick Mosteller

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