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Publisher:

Dover Publications

Publication Date:

1987

Number of Pages:

88

Format:

Paperback

Price:

6.95

ISBN:

978-0486653556

Category:

Problem Book

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by , on ]

Brian Borchers

07/6/2010

This book is a collection of 56 elementary problems in probability theory, together with their solutions. The problems are presented in the style of recreational mathematics puzzles rather than dry textbook exercises. Although many of the problems have no broader applicability, some of the problems, particularly the problems on random walks in two and three dimensions, have significant applications. Some of the problems are also of historical interest. For example, Mosteller includes a problem involving a dice game that Samuel Pepys asked Isaac Newton about in a letter written in 1693. Most of the problems can be solved using nothing more than algebra. A few problems require some calculus. This book is highly recommended for upper level high school students and lower level undergraduates. Teachers will also find it to be a great source of enrichment material.

Brian Borchers is a professor of Mathematics at the New Mexico Institute of Mining and Technology. His interests are in optimization and applications of optimization in parameter estimation and inverse problems.

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 |

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