Probability interview questions: page 2 of 19

Questions 51–100

51. Markov chain return time to a bad bagelEasy
52. One optional redraw of a uniform numberEasy
53. Two hunters with one bullet each walking to a targetHard
54. Gambler's ruin with a two-thirds coinEasy
55. Rolls until neighbouring values are within oneHard
56. Ten tosses where tails only come in pairsMedium
57. Two red then two blue jellybeansEasy
58. Geometric mean of many uniformsMedium
59. Break-even chance of striking oilEasy
60. Climbing ten steps using only odd-sized jumpsMedium
61. Upward-biased walk ever reaching +1Medium
62. Tosses until one face appears three timesMedium
63. Card value or a fixed 3.50 dollarsEasy
64. Odd head count from a hundred coinsMedium
65. Distinct prizes from seven cereal boxesHard
66. Guessing colours of two red and two blue orbsMedium
67. Sum of seven with a dot-weighted dieEasy
68. Parity of three pairwise products from 1 to 6Medium
69. At least one couple matched in random pairingMedium
70. When to call a doubled sports wagerEasy
71. Seeker's first spot turning up emptyEasy
72. Most likely position of the fifth king in a shoeMedium
73. Variance of the optimal pick in a two-below gameMedium
74. Colour of the final cherry eaten from two bowlsHard
75. Newborn's sex after a boy is picked from the nurseryEasy
76. Two uniforms in the same dyadic bandMedium
77. Reroll for the sum but pay if it reaches sevenMedium
78. Relabelled dice that can hit every sum 2 to 12Medium
79. Six odd parts summing to 96Medium
80. At least four Poisson arrivals in an hourEasy
81. How many paid bidders to recruitMedium
82. Expected rolls to see a 5 followed by a 6Easy
83. One geometric wait at least four times anotherMedium
84. Two random arcs on a circle not overlappingHard
85. Pricing an option on a house's future valueMedium
86. Covariance from variances of sum and differenceEasy
87. Optional cash-out in a roll-until-5-or-6 gameMedium
88. Chance of being dealt three of a kindMedium
89. Expected area of a field with measurement errorsEasy
90. Eight coins with one optional reflip eachEasy
91. Chance two uniforms multiply to more than a halfEasy
92. Bond percolation on the square lattice: a union boundMedium
93. Alternating die game with unequal winning facesEasy
94. Recovering a coin bias from a posterior odds ratioMedium
95. Normal tail two standard deviations above the meanEasy
96. Second blue draw from a randomly chosen bowlEasy
97. Expected arc covering a fixed point of the circleHard
98. Four people drawing five of seventeen balls overlapHard
99. Cutting chain links until only the top orb is leftHard
100. Dice duel where ties win and one outcome forces a rerollEasy