Can you solve the problem of "The Unfair Subway"? Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain. Marvin's adventures ...
Can you solve the problem of "The Unfair Subway"? Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain.
Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to challenge the mathematically inclined. From "The Flippant Juror" and "The Prisoner's Dilemma" to "The Cliffhanger" and "The Clumsy Chemist," they provide an ideal supplement for all who enjoy the stimulating fun of mathematics.
Professor Frederick Mosteller, who teaches statistics at Harvard University, has chosen the problems for originality, general interest, or because they demonstrate valuable techniques. In addition, the problems are graded as to difficulty and many have considerable stature. Indeed, one has "enlivened the research lives of many excellent mathematicians." Detailed solutions are included. There is every probability you'll need at least a few of them.
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 drawer
2. Successive wins
3. The flippant juror
4. Trials until first success
5. Coin in square
7. Curing the compulsive gambler
8. Perfect bridge hand
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