Fifty Challenging Problems in Probability with Solutions

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

• 1. The sock drawer2. Successive wins3. The flippant juror4. Trials until first success5. Coin in square6. Chuck-a-luck7. Curing the compulsive gambler8. Perfect bridge hand9. Craps10. An experiment in personal taste for money11. Silent cooperation12. Quo vadis?13. The prisoner's dilemma14. "Collecting coupons, including Euler's approximation for harmonic sums"15. The theater row16. Will second-best be runner-up?17. Twin knights18. "An even split at coin tossing, including Stirling's approximation"19. Isaac Newton helps Samuel Pepys20. The three-cornered duel21. Should you sample with or without replacement?22. The ballot box23. Ties in matching pennies24. The unfair subway25. Lengths of random chords26. The hurried duelers27. Catching the cautious counterfeiter28. "Catching the greedy counterfeiter, including the Poisson distribution"29. Moldy gelation30. Evening the sales31. Birthday pairings32. Finding your birthmate33. Relating the birthday pairings and birthmate problems34. Birthday holidays35. The cliff-hanger36. Gambler's ruin37. Bold play vs. cautious play38. The thick coin Digression: A note on the principle of symmetry when points are dropped on a line 39. The clumsy chemist40. The first ace41. The locomotive problem42. The little end of the stick43. The broken bar44. Winning an unfair game45. Average number of matches46. Probabilities of matches47. Choosing the largest dowry48. Choosing the largest random number49. Doubling your accuracy50. Random quadratic equations51. Two-dimensional random walk52. Three-dimensional random walk53. Buffon's needle54. Buffon's needle with horizontal and vertical rulings55. Long needles56. Molina's urns