Fifty Challenging Problems in Probability with Solutions

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