170 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
  8. 08All DifferentEasy
  9. 09Strictly Increasing RollsMedium · Private
  10. 10The Birthday ParadoxMedium
  11. 11The Suspicious CoinMedium · Private
  12. 12Full HouseMedium · Private
  13. 13Gambler's RuinMedium
  14. 14The Lost Boarding PassMedium · Private
  15. 15Amoeba ExtinctionHard · Private
  16. 16The Hat Check ProblemMedium
  17. 17The Broken StickHard
  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
  36. 36Three PrisonersMedium
  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
  50. 50Always in the LeadHard · Private
  51. 51Two MatchboxesHard
  52. 52Hire the BestHard
  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
  60. 60Buffon's NeedleHard
  61. 61HH Before HTMedium
  62. 62Still WaitingEasy
  63. 63Which Breaks FirstEasy
  64. 64Calm and StormEasy
  65. 65Tight Stop, Far TargetMedium · Private
  66. 66Back-to-Back SixesMedium · Private
  67. 67Thinning the TapeMedium · Private
  68. 68Counting the CyclesMedium · Private
  69. 69Two Heads of EvidenceMedium
  70. 70Fourth Order InMedium · Private
  71. 71The Last Blue MarbleMedium · Private
  72. 72Will the Cascade Die?Medium · Private
  73. 73Cover Both VenuesMedium · Private
  74. 74Three Fills, Ten MinutesMedium · Private
  75. 75High-Water MarkMedium · Private
  76. 76Last One OutMedium · Private
  77. 77Spread of the MatchesMedium · Private
  78. 78Grinding UphillHard · Private
  79. 79The Alternating PatternHard · Private
  80. 80Quit While AheadHard · Private
  81. 81Call the Next CardHard · Private
  82. 82Peak of the PathHard · Private
  83. 83Crossing the Same TickHard · Private
  84. 84Fresh GroundHard · Private
  85. 85Never Behind on the TapeHard · Private
  86. 86Race from the Same TriggerHard · Private
  87. 87The Wandering KingHard · Private
  88. 88Floor and TargetHard · Private
  89. 89Three Weathers of the MarketHard · Private
  90. 90Tenth Draw from a Rich-Get-Richer UrnHard · Private
  91. 91Where the Urn SettlesHard · Private
  92. 92Pair of SuspectsHard · Private
  93. 93The Longest ShardHard · Private
  94. 94No Two Too CloseHard · Private
  95. 95Waiting on the SlowestHard · Private
  96. 96The Gap You Land InHard · Private
  97. 97Three Alphas Before Two BetasHard · Private
  98. 98Collecting Lopsided CouponsHard · Private
  99. 99Two Coupons per BoxHard · Private
  100. 100Does the Rare One Finish Last?Hard · Private
  101. 101Exactly Two HighsHard · Private
  102. 102The Chain You Stand InHard · Private
  103. 103The Cancellation StormHard · Private
  104. 104Given the Index JumpedHard · Private
  105. 105Quadrant OddsHard · Private
  106. 106Race with a Head StartHard · Private
  107. 107Price the Four-Sigma DayHard · Private
  108. 108Stopped at the First TailHard · Private
  109. 109Two Alarms, One AccountHard · Private
  110. 110Dead Center of Four DiceHard · Private
  111. 111A Hundred Dice, Modulo SixHard · Private
  112. 112The Average That RefusesHard · Private
  113. 113Volatility of a Busy DayHard · Private
  114. 114Last Stop on the RingHard · Private
  115. 115How Uncertain Is the ClimbHard · Private
  116. 116The Split Behind the PrintHard · Private
  117. 117Above the ThresholdEasy
  118. 118Fastest of ThreeEasy
  119. 119Two Scanners, One WinnerMedium · Private
  120. 120Second Six, Seventh RollMedium · Private
  121. 121Back to the StartMedium · Private
  122. 122Three Badges, Three LoopsMedium · Private
  123. 123Three on One DayMedium · Private
  124. 124The Squared ShockMedium · Private
  125. 125One Switch in Five DaysMedium · Private
  126. 126Two Heads, One Tail of EvidenceMedium · Private
  127. 127Ask the Right QuestionsMedium · Private
  128. 128A Month Without a Two-Sigma DayMedium · Private
  129. 129How Far Past the ThresholdHard · Private
  130. 130When the Winner FillsHard · Private
  131. 131One Loop to Rule ThemHard · Private
  132. 132Nobody Home, Given One MissHard · Private
  133. 133The First Gap WinsHard · Private
  134. 134How Noisy Are RecordsHard · Private
  135. 135Spread of the StreaksHard · Private
  136. 136Variance of the CoincidencesHard · Private
  137. 137Almost the Same BirthdayHard · Private
  138. 138Collisions on the Hot VenueHard · Private
  139. 139Stop at the Big StakeHard · Private
  140. 140Below the Squared SignalHard · Private
  141. 141Product of Two UniformsHard · Private
  142. 142The Ratio That Has No MeanHard · Private
  143. 143Mean Squared SeparationHard · Private
  144. 144Fastest, Middle, SlowestHard · Private
  145. 145The Worst Day of the YearHard · Private
  146. 146Odds of a Quiet DayHard · Private
  147. 147Two Calls Up, One Call DownHard · Private
  148. 148The Price of RejectionHard · Private
  149. 149Inside the Gaussian CircleHard · Private
  150. 150Waiting for HTHTHard · Private
  151. 151Both Streaks ObservedHard · Private
  152. 152Same Seeds, Different RulesHard · Private
  153. 153Drawdown in Four TicksHard · Private
  154. 154Will the Edge Show Up?Hard · Private
  155. 155Counting the Up-MovesHard · Private
  156. 156Guess the Cap from the FillHard · Private
  157. 157Until Both SucceedHard · Private
  158. 158Reviews Until ApprovalHard · Private
  159. 159All Aces Before Any KingHard · Private
  160. 160Nothing in the First TenthHard · Private
  161. 161The Opening Tick, Seen from the CloseHard · Private
  162. 162What the One-Liner GeneratesHard · Private
  163. 163Cancel at Six SecondsHard · Private
  164. 164An Even Total, an Uneven Split?Hard · Private
  165. 165HHTT versus HTHTHard · Private
  166. 166Which Path Sent the Ack?Hard · Private
  167. 167The Lost Boarding PassMedium
  168. 168You Pick SecondHard · Private
  169. 169Five Reds in a RowEasy
  170. 170The Survey That LiesMedium · Private