← Question bank

168 questions · full solutions

Probability

The core of every trading interview. Dice, cards, conditioning, Bayes, random walks, and the geometric classics, each solved the way an interviewer wants to hear it: structure first, then the computation.

  1. 01Sum of SevenEasy
  2. 02At Least One SixEasy
  3. 03Conditioned DieEasy
  4. 04Two Red CardsEasy
  5. 05Beat My RollEasy
  6. 06The Two-Child ProblemEasy
  7. 07Monty HallMedium · Private
  8. 08All DifferentEasy
  9. 09Strictly Increasing RollsMedium · Private
  10. 10The Birthday ParadoxMedium · Private
  11. 11The Suspicious CoinMedium · Private
  12. 12Full HouseMedium · Private
  13. 13Gambler's RuinMedium · Private
  14. 14The Lost Boarding PassMedium · Private
  15. 15Amoeba ExtinctionHard · Private
  16. 16The Hat Check ProblemMedium · Private
  17. 17The Broken StickHard · Private
  18. 18Points on a SemicircleHard · Private
  19. 19Parity LockEasy
  20. 20First Head WinsEasy
  21. 21Ace in the HandEasy
  22. 22Socks in the DarkEasy
  23. 23The Positive TestEasy
  24. 24Highest of ThreeEasy
  25. 25Three Coins, Partial NewsEasy
  26. 26Different DiceEasy
  27. 27The Thirteenth CardEasy
  28. 28Waiting for the FillEasy
  29. 29Seven Before EightMedium · Private
  30. 30Exactly Fifty-FiftyMedium · Private
  31. 31How Many Heads to Believe?Medium · Private
  32. 32The TellMedium · Private
  33. 33The Night-Time WitnessMedium · Private
  34. 34One in a Hundred ThousandMedium · Private
  35. 35The Better DeskMedium · Private
  36. 36Three PrisonersMedium · Private
  37. 37The Gap Between Two QuotesMedium · Private
  38. 38The Fifteen-Minute MeetingMedium · Private
  39. 39Back Where It StartedMedium · Private
  40. 40Three Up or Two DownMedium · Private
  41. 41The Reinforcing UrnMedium · Private
  42. 42Record HighsMedium · Private
  43. 43The Middle DrawMedium · Private
  44. 44Spread of ThreeMedium · Private
  45. 45Every Face in Ten RollsMedium · Private
  46. 46Shooting StarsMedium · Private
  47. 47The Red FaceMedium · Private
  48. 48Three Green DaysMedium · Private
  49. 49The Hundred BoxesHard · Private
  50. 50Always in the LeadHard · Private
  51. 51Two MatchboxesHard · Private
  52. 52Hire the BestHard · Private
  53. 53The Pattern RaceHard · Private
  54. 54Landing on TenHard · Private
  55. 55Never UnderwaterHard · Private
  56. 56Pricing the Pass LineHard · Private
  57. 57No Way BackHard · Private
  58. 58Random QuadraticHard · Private
  59. 59The Random ChordHard · Private
  60. 60Buffon's NeedleHard · Private
  61. 61Still WaitingEasy
  62. 62Which Breaks FirstEasy
  63. 63Calm and StormEasy
  64. 64Tight Stop, Far TargetMedium · Private
  65. 65Back-to-Back SixesMedium · Private
  66. 66Thinning the TapeMedium · Private
  67. 67Counting the CyclesMedium · Private
  68. 68Two Heads of EvidenceMedium · Private
  69. 69Fourth Order InMedium · Private
  70. 70The Last Blue MarbleMedium · Private
  71. 71Will the Cascade Die?Medium · Private
  72. 72Cover Both VenuesMedium · Private
  73. 73Three Fills, Ten MinutesMedium · Private
  74. 74High-Water MarkMedium · Private
  75. 75Last One OutMedium · Private
  76. 76Spread of the MatchesMedium · Private
  77. 77Grinding UphillHard · Private
  78. 78The Alternating PatternHard · Private
  79. 79Quit While AheadHard · Private
  80. 80Call the Next CardHard · Private
  81. 81Peak of the PathHard · Private
  82. 82Crossing the Same TickHard · Private
  83. 83Fresh GroundHard · Private
  84. 84Never Behind on the TapeHard · Private
  85. 85Race from the Same TriggerHard · Private
  86. 86The Wandering KingHard · Private
  87. 87Floor and TargetHard · Private
  88. 88Three Weathers of the MarketHard · Private
  89. 89Tenth Draw from a Rich-Get-Richer UrnHard · Private
  90. 90Where the Urn SettlesHard · Private
  91. 91Pair of SuspectsHard · Private
  92. 92The Longest ShardHard · Private
  93. 93No Two Too CloseHard · Private
  94. 94Waiting on the SlowestHard · Private
  95. 95The Gap You Land InHard · Private
  96. 96Three Alphas Before Two BetasHard · Private
  97. 97Collecting Lopsided CouponsHard · Private
  98. 98Two Coupons per BoxHard · Private
  99. 99Does the Rare One Finish Last?Hard · Private
  100. 100Exactly Two HighsHard · Private
  101. 101The Chain You Stand InHard · Private
  102. 102The Cancellation StormHard · Private
  103. 103Given the Index JumpedHard · Private
  104. 104Quadrant OddsHard · Private
  105. 105Race with a Head StartHard · Private
  106. 106Price the Four-Sigma DayHard · Private
  107. 107Stopped at the First TailHard · Private
  108. 108Two Alarms, One AccountHard · Private
  109. 109Dead Center of Four DiceHard · Private
  110. 110A Hundred Dice, Modulo SixHard · Private
  111. 111The Average That RefusesHard · Private
  112. 112Volatility of a Busy DayHard · Private
  113. 113Last Stop on the RingHard · Private
  114. 114How Uncertain Is the ClimbHard · Private
  115. 115The Split Behind the PrintHard · Private
  116. 116Above the ThresholdEasy
  117. 117Fastest of ThreeEasy
  118. 118Two Scanners, One WinnerMedium · Private
  119. 119Second Six, Seventh RollMedium · Private
  120. 120Back to the StartMedium · Private
  121. 121Three Badges, Three LoopsMedium · Private
  122. 122Three on One DayMedium · Private
  123. 123The Squared ShockMedium · Private
  124. 124One Switch in Five DaysMedium · Private
  125. 125Two Heads, One Tail of EvidenceMedium · Private
  126. 126Ask the Right QuestionsMedium · Private
  127. 127A Month Without a Two-Sigma DayMedium · Private
  128. 128How Far Past the ThresholdHard · Private
  129. 129When the Winner FillsHard · Private
  130. 130One Loop to Rule ThemHard · Private
  131. 131Nobody Home, Given One MissHard · Private
  132. 132The First Gap WinsHard · Private
  133. 133How Noisy Are RecordsHard · Private
  134. 134Spread of the StreaksHard · Private
  135. 135Variance of the CoincidencesHard · Private
  136. 136Almost the Same BirthdayHard · Private
  137. 137Collisions on the Hot VenueHard · Private
  138. 138Stop at the Big StakeHard · Private
  139. 139Below the Squared SignalHard · Private
  140. 140Product of Two UniformsHard · Private
  141. 141The Ratio That Has No MeanHard · Private
  142. 142Mean Squared SeparationHard · Private
  143. 143Fastest, Middle, SlowestHard · Private
  144. 144The Worst Day of the YearHard · Private
  145. 145Odds of a Quiet DayHard · Private
  146. 146Two Calls Up, One Call DownHard · Private
  147. 147The Price of RejectionHard · Private
  148. 148Inside the Gaussian CircleHard · Private
  149. 149Waiting for HTHTHard · Private
  150. 150Both Streaks ObservedHard · Private
  151. 151Same Seeds, Different RulesHard · Private
  152. 152Drawdown in Four TicksHard · Private
  153. 153Will the Edge Show Up?Hard · Private
  154. 154Counting the Up-MovesHard · Private
  155. 155Guess the Cap from the FillHard · Private
  156. 156Until Both SucceedHard · Private
  157. 157Reviews Until ApprovalHard · Private
  158. 158All Aces Before Any KingHard · Private
  159. 159Nothing in the First TenthHard · Private
  160. 160The Opening Tick, Seen from the CloseHard · Private
  161. 161What the One-Liner GeneratesHard · Private
  162. 162Cancel at Six SecondsHard · Private
  163. 163An Even Total, an Uneven Split?Hard · Private
  164. 164HHTT versus HTHTHard · Private
  165. 165Which Path Sent the Ack?Hard · Private
  166. 166You Pick SecondHard · Private
  167. 167Five Reds in a RowEasy
  168. 168The Survey That LiesMedium · Private