← Interview questions (18) 168 questions Choose a title to open its card
P001 The three-outcome contractExpectation Easy ↗ P002 A basket of diceExpectation Easy ↗ P003 The double-six ticketCounting Easy ↗ P004 An odd productCounting Easy ↗ P005 A product divisible by threeCounting Easy ↗ P006 Same-colour pairCards Easy ↗ P007 Aces in a short handCards Easy ↗ P008 The exposed red cardCards Easy ↗ P009 Waiting for an eightWaiting times Easy ↗ P010 Three successful fillsWaiting times Easy ↗ P011 At least one fillCounting Easy ↗ P012 Which coin did you choose?Bayes Easy ↗ P013 The rare alertBayes Easy ↗ P014 A sum with a known dieConditioning Easy ↗ P015 At least one headConditioning Easy ↗ P016 Keep four or reroll?Strategy Easy ↗ P017 An expensive second chanceStrategy Easy ↗ P018 A winning bet that loses moneyFair pricing Easy ↗ P019 The break-even entry feeFair pricing Easy ↗ P020 Two identical marginalsRisk Easy ↗ P021 Scaling a positionRisk Easy ↗ P022 A simple hedgeRisk Easy ↗ P023 Matching envelopesExpectation Easy ↗ P024 Occupied venuesExpectation Easy ↗ P025 Adjacent matching rollsExpectation Easy ↗ P026 A uniform quoteContinuous probability Easy ↗ P027 The better of two estimatesContinuous probability Easy ↗ P028 Which uniform number is larger?Continuous probability Easy ↗ P029 No messages this minuteArrivals Easy ↗ P030 How much longer?Arrivals Easy ↗ P031 An optional purchaseStrategy Easy ↗ P032 A perfect previewInformation Easy ↗ P033 Two sides of one eventFair pricing Easy ↗ P034 The nested eventsFair pricing Easy ↗ P035 The first move of a walkRandom walks Easy ↗ P036 Returning in two stepsRandom walks Easy ↗ P037 Exactly two winnersCounting Easy ↗ P038 A win after a losing streakConditioning Easy ↗ P039 A random-length basketExpectation Easy ↗ P040 A red-black forecastCards Easy ↗ P041 A duplicate in three drawsCounting Easy ↗ P042 Shared birthdaysExpectation Easy ↗ P043 A Bernoulli payoutRisk Easy ↗ P044 Choose your dieStrategy Easy ↗ P045 The hidden regimeConditioning Easy ↗ P046 A capped waitWaiting times Easy ↗ P047 A maximum on a tiny dieExpectation Easy ↗ P048 An uninformative signalInformation Easy ↗ P049 Adding a transaction feeFair pricing Easy ↗ P050 Diversification without a free lunchRisk Easy ↗ P051 The value of one rerollStrategy Medium ↗ P052 Three chances, no recallStrategy Medium ↗ P053 Pay for unlimited rerollsStrategy Medium ↗ P054 The four-symbol collectorWaiting times Medium ↗ P055 Two consecutive headsWaiting times Medium ↗ P056 A head then a tailWaiting times Medium 🔒 P057 The first marked cardCards Medium 🔒 P058 Two heads from a mixed boxBayes Medium 🔒 P059 Learning an unknown fill rateBayes Medium 🔒 P060 A known sumConditioning Medium 🔒 P061 The higher quoteOrder statistics Medium 🔒 P062 The gap between quotesOrder statistics Medium 🔒 P063 A meeting windowContinuous probability Medium 🔒 P064 Which feed arrives first?Arrivals Medium 🔒 P065 Filtering the flowArrivals Medium 🔒 P066 A hidden-market mixtureRisk Medium 🔒 P067 Two correlated positionsRisk Medium 🔒 P068 Choosing a hedge sizeRisk Medium 🔒 P069 Kelly on a favourable coinStrategy Medium 🔒 P070 A noisy previewInformation Medium 🔒 P071 The informed sellerAdverse selection Medium 🔒 P072 Valuable to a different ownerAdverse selection Medium 🔒 P073 A product divisible by fourCounting Medium 🔒 P074 Exactly one pairCounting Medium 🔒 P075 Every letter misplacedCounting Medium 🔒 P076 A small ruin problemRandom walks Medium 🔒 P077 A biased ruin problemRandom walks Medium 🔒 P078 First repeated symbolWaiting times Medium 🔒 P079 Records in a price sequenceExpectation Medium 🔒 P080 The largest is above a thresholdConditioning Medium 🔒 P081 A sampled die averageRisk Medium 🔒 P082 A capped die payoffFair pricing Medium 🔒 P083 Buying a reroll couponStrategy Medium 🔒 P084 A risk of losing the potStrategy Medium 🔒 P085 An unknown coin after a streakBayes Medium 🔒 P086 Red cards are negatively linkedCards Medium 🔒 P087 Collision pairs across venuesExpectation Medium 🔒 P088 Two events before the deadlineArrivals Medium 🔒 P089 A triangular sumContinuous probability Medium 🔒 P090 Price a random sampleFair pricing Medium 🔒 P091 A red-black stopping choiceStrategy Medium 🔒 P092 Race to a faceRandom walks Medium 🔒 P093 The exploding dieWaiting times Medium 🔒 P094 A total count is knownConditioning Medium 🔒 P095 Second-best of fourOrder statistics Medium 🔒 P096 A fee to see the alternativeStrategy Medium 🔒 P097 A rare large lossRisk Medium 🔒 P098 The quoted posteriorInformation Medium 🔒 P099 A circular neighbour matchCounting Medium 🔒 P100 Commit before observingStrategy Medium 🔒 P101 One reroll, a product payoffStrategy Hard ↗ P102 Unlimited uniform replacementsStrategy Hard ↗ P103 Two optional retries with a feeStrategy Hard ↗ P104 A two-step bank-or-bust gameStrategy Hard 🔒 P105 Previewing whether a reroll is highInformation Hard 🔒 P106 Two noisy opinionsInformation Hard 🔒 P107 A mixture of informed and noise buyersAdverse selection Hard 🔒 P108 A bid with resale value and a capAdverse selection Hard 🔒 P109 Learning from a fillAdverse selection Hard 🔒 P110 Two fills from a persistent regimeBayes Hard 🔒 P111 The uncertainty that survives diversificationBayes Hard 🔒 P112 Buy one experiment?Bayes Hard 🔒 P113 A tiny unknown-coin banditStrategy Hard 🔒 P114 Exploration with a weaker safe coinStrategy Hard 🔒 P115 The pattern HTHWaiting times Hard 🔒 P116 Three consecutive headsWaiting times Hard 🔒 P117 A pattern race is not a waiting-time raceWaiting times Hard 🔒 P118 Unequal coupon probabilitiesWaiting times Hard 🔒 P119 The collector with a free choiceWaiting times Hard 🔒 P120 The last marked cardCards Hard 🔒 P121 Optimal prediction without replacementCards Hard 🔒 P122 Stopping a balanced token gameStrategy Hard 🔒 P123 A gap conditional on the maximumOrder statistics Hard 🔒 P124 Uniform range riskOrder statistics Hard 🔒 P125 Win probability or expected score?Strategy Hard 🔒 P126 How many buys before a sell?Arrivals Hard 🔒 P127 The bus that an observer seesArrivals Hard 🔒 P128 Random number of tradesRisk Hard 🔒 P129 Why uncorrelated is not independentRisk Hard 🔒 P130 The random-sum stopping trapRisk Hard 🔒 P131 A walk around a hexagonRandom walks Hard 🔒 P132 Covering a cycleRandom walks Hard 🔒 P133 A biased walk's durationRandom walks Hard 🔒 P134 Independent pairs, dependent tripleCounting Hard 🔒 P135 Variance of occupied venuesCounting Hard 🔒 P136 Exactly one shared venue pairCounting Hard 🔒 P137 Breaking a stick into threeExpectation Hard 🔒 P138 The longest side of a random triangleContinuous probability Hard 🔒 P139 A best-of-three stopping contestStrategy Hard 🔒 P140 Reject a sample, then take a recordStrategy Hard 🔒 P141 A repeated bet with unequal oddsStrategy Hard 🔒 P142 Replication on three statesFair pricing Hard 🔒 P143 Pairwise independence still leaves a price rangeFair pricing Hard 🔒 P144 A biased coin made fairInformation Hard 🔒 P145 Waiting to beat the first observationWaiting times Hard 🔒 P146 A one-use safety shieldStrategy Hard 🔒 P147 Pay to improve the closest quoteStrategy Hard 🔒 P148 When a nonlinear hedge beats a linear oneRisk Hard 🔒 P149 An optimal offer with uncertain competitionStrategy Hard 🔒 P150 A signal that removes adverse selectionInformation Hard 🔒 P151 The queue that keeps changingStrategy · MULTI-PART Hard 🔒 P152 A research report with a second opinionInformation · MULTI-PART Hard 🔒 P153 The price that attracts the wrong tradesAdverse selection · MULTI-PART Hard 🔒 P154 One spare reroll for the whole deskStrategy · MULTI-PART Hard 🔒 P155 Should the desk explore an unknown venue?Bayes · MULTI-PART Hard 🔒 P156 Collect, pay, or keep drawingWaiting times · MULTI-PART Hard 🔒 P157 Many trades, one hidden marketRisk · MULTI-PART Hard 🔒 P158 A fair game with an unfair stopping argumentStrategy · MULTI-PART Hard 🔒 P159 The fastest route is not always the best raceInformation · MULTI-PART Hard 🔒 P160 Pick the feed, then pick the hedgeArrivals · MULTI-PART Hard 🔒 P161 Stop for a target or build a bigger handStrategy · MULTI-PART Hard 🔒 P162 Can all three probability quotes be right?Fair pricing · MULTI-PART Hard 🔒 P163 An unknown coin becomes a uniform integerRandom generation · MULTI-PART Hard 🔒 P164 Recycle the rejected dice outcomesRandom generation · MULTI-PART Hard 🔒 P165 A loaded die without known face probabilitiesRandom generation · MULTI-PART Hard 🔒 P166 Shuffle cards with only an unknown coinRandom generation · MULTI-PART Hard 🔒 P167 When the coin's bias driftsRandom generation · MULTI-PART Hard 🔒 P168 An exact three-in-ten eventRandom generation · MULTI-PART Hard 🔒 About this collection & research sources Original practice wording informed by the Quant Trading Guide, A Collection of Dice Problems, A Practical Guide to Quantitative Finance Interviews, and the sources below. The queue case is a precisely defined variant inspired by a user's recollection, not a reconstruction of an actual interview.
Jane Street: Probability & Markets · Washington CSE 312: Fairness from a biased coin · Harvard Stat 110 · MIT probability
Difficulty is an editorial guide. These are practice problems, not claims about questions asked by a particular firm. Read the stated assumptions carefully; a different model can change the answer.