You are here

Fifty Challenging Problems in Probability with Solutions

Frederick Mosteller
Dover Publications
Publication Date: 
Number of Pages: 
Problem Book
BLL Rating: 

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

[Reviewed by
Brian Borchers
, on

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