Fifty Challenging Problems in Probability with Solutions

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Fifty Challenging Problems in Probability with Solutions

Frederick Mosteller

(1987)

Sprog: Engelsk

Dover Publications, Incorporated

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Paperback: 96 sider
Udgiver: Dover Publications, Incorporated (Maj 1987)
ISBN: 9780486653556

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Indhold

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.

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

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