Probability & Market-Making Interview Questions
Probability-and-market-making interviews centre on expected value and fast mental arithmetic, wrapped in betting-game and quoting scenarios that test how you price and manage risk under uncertainty.
Expect to reason out loud through probability and expected-value problems, price simple betting games, and rattle off quick mental arithmetic - frequently with a market-making twist where you quote a fair price and update as new information arrives. Coding and data-analysis questions appear for technology and research roles.
Rounds of this kind typically care as much about your method as your final answer. Prior finance knowledge is rarely assumed; what is being sampled is how you handle uncertainty, so practise narrating your reasoning rather than only producing a number.
398 questions tagged to Probability & Market-Making · 276 free to practise now.
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This format leans on probability, expected value, and quoting intuition. These NeetQuant tools target exactly those skills:
- A coin that branches into a dieEasyCombinatoricsExpected ValueView →
- A divisor of a power of tenEasyProbabilityCombinatoricsView →
- A factorial ratio that's a factorialEasyBrainteasersView →
- A majority of onesEasyCombinatoricsView →
- A mixed second partial derivativeEasyCalculusView →
- A multiple of 15 in ones and zerosEasyBrainteasersView →
- A ratio of Fibonacci sumsEasyBrainteasersView →
- A root of a product plus oneEasyBrainteasersView →
- A specific sequence given three headsEasyProbabilityConditional Probability & ExpectationView →
- A sum of three cubesEasyBrainteasersView →
- Age in a square yearEasyBrainteasersView →
- All four aces before any kingEasyProbabilityCombinatoricsView →
- All the squares on a chessboardEasyCombinatoricsBrainteasersView →
- An alternating sum of squaresEasyBrainteasersView →
- An infinite nested radicalEasyBrainteasersView →
- An odd subset with two small elementsEasyCombinatoricsView →
- Arranging colored balls in a lineEasyCombinatoricsView →
- Beating a product of uniformsEasyProbabilityRandom VariablesView →
- Beating three othersEasyProbabilityRandom VariablesView →
- Chebyshev on a concrete intervalEasyStatisticsView →
- Clock angle at 3:15EasyBrainteasersView →
- Correlation of two event indicatorsEasyProbabilityStatisticsView →
- Counting 8-bit stringsEasyCombinatoricsView →
- Counting complement pairsEasyProgramming & DSAView →
- Counting nines to 1000EasyCombinatoricsBrainteasersView →
- Counting up-down walks to a targetEasyCombinatoricsView →
- Crossing the origin twiceEasyStochastic ProcessesView →
- Depth of a key in a BSTEasyProgramming & DSAView →
- Determinant from trace and one eigenvalueEasyLinear AlgebraView →
- Determinant of a scaled productEasyLinear AlgebraView →
- Diagonal parameter from a triangular determinantEasyLinear AlgebraView →
- Eigenvalues of a 2×2 matrixEasyLinear AlgebraView →
- Even heads with one fair coinEasyProbabilityConditional Probability & ExpectationView →
- Expected flips for two heads in a rowEasyProbabilityExpected ValueView →
- Guessing a number with high-low hintsEasyBrainteasersProgramming & DSAView →
- Handshakes at four couplesEasyCombinatoricsBrainteasersView →
- Integers that contain a zeroEasyCombinatoricsBrainteasersView →
- Keep it or draw againEasyProbabilityExpected ValueView →
- Largest eigenvalue after squaringEasyLinear AlgebraView →
- Lattice paths through a checkpointEasyCombinatoricsView →
- Matching a max and a min at zeroEasyProbabilityView →
- Matching locks to keysEasyBrainteasersView →
- Maximum subarray sumEasyProgramming & DSAView →
- More heads than tails in six flipsEasyProbabilityView →
- Peak depth times group count of a bracket scanEasyProgramming & DSAView →
- Polygons with integer anglesEasyBrainteasersView →
- Reflipping for valueEasyProbabilityExpected ValueView →
- Repeated digit on a plateEasyCombinatoricsView →
- Retries under a hard capEasyExpected ValueStochastic ProcessesView →
- Six heads from a random biased coinEasyConditional Probability & ExpectationRandom VariablesView →
- Solving a linear Diophantine equationEasyBrainteasersView →
- Summing n plus one over two to the nEasyCalculusView →
- Tangent-minus-sine third-order limitEasyCalculusView →
- The added babyEasyProbabilityConditional Probability & ExpectationView →
- The largest unmakeable postageEasyBrainteasersView →
- The price of a triangular gardenEasyBrainteasersView →
- The top two cards form a pairEasyProbabilityCombinatoricsView →
- The two missing numbersEasyProgramming & DSAView →
- Three cube faces at a cornerEasyProbabilityCombinatoricsView →
- Two primes with an even sumEasyProbabilityCombinatoricsView →
- Unchanged after ten swingsEasyProbabilityBrainteasersView →
- Units digit of a random productEasyProbabilityCombinatoricsView →
- Weighting a fixed sumEasyConditional Probability & ExpectationExpected ValueView →
- When the clock hands next meetEasyBrainteasersView →
- Where the arrivals landEasyProbabilityStochastic ProcessesView →
- Whether either bus comes soonEasyProbabilityRandom VariablesView →
- 25 horses, 5 tracksMediumBrainteasersView →
- A cube ending in elevenMediumProbabilityBrainteasersView →
- A low medianMediumProbabilityRandom VariablesView →
- A point near the cone's baseMediumProbabilityCalculusView →
- A prime sum on prime diceMediumProbabilityCombinatoricsView →
- Adults before the busMediumBrainteasersView →
- Age a fraction of the birth yearMediumBrainteasersView →
- An ace for everyoneMediumProbabilityCombinatoricsView →
- An ace in every pileMediumProbabilityCombinatoricsView →
- An ant returning to its cornerMediumExpected ValueStochastic ProcessesView →
- Anagrams of LOLLIPOPMediumCombinatoricsView →
- Balanced parenthesesMediumCombinatoricsProgramming & DSAView →
- Best linear blend of two estimatesMediumRandom VariablesStatisticsView →
- Boy–girl neighbors in a lineMediumCombinatoricsExpected ValueView →
- Cats and dogs on the streetMediumBrainteasersView →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Clock hands overlapMediumBrainteasersView →
- Coin sets the number of dice rollsMediumProbabilityConditional Probability & ExpectationView →
- Cosine of a conditional meanMediumProbabilityConditional Probability & ExpectationView →
- Cutting a cube into 27MediumBrainteasersView →
- Deleting every other number on a circleMediumCombinatoricsBrainteasersView →
- Density of a uniform squaredMediumRandom VariablesCalculusView →
- Derivative of xˣMediumCalculusView →
- Digits multiplying to half the numberMediumBrainteasersView →
- Digits of concatenated powersMediumBrainteasersView →
- Distinct die labelingsMediumCombinatoricsBrainteasersView →
- Distributing candies with a capMediumCombinatoricsView →
- Eigenvalues of a projectionMediumLinear AlgebraView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- Exactly two aces in a bridge handMediumProbabilityCombinatoricsView →
- Expected fives before the first sixMediumProbabilityExpected ValueView →
- Expected flips for HHMediumRandom VariablesExpected ValueView →
- Expected flips for HTMediumExpected ValueStochastic ProcessesView →
- Fair outcome from a biased coinMediumProbabilityStatisticsView →
- First HH on the tenth tossMediumProbabilityCombinatoricsView →
- First head strictly soonerMediumProbabilityRandom VariablesView →
- First passage to ±1MediumStochastic ProcessesView →
- First to three of a kind in a rowMediumProbabilityExpected ValueView →
- Four fives before the first sixMediumProbabilityRandom VariablesView →
- Four points on a semicircleMediumProbabilityView →
- Four times as long to the first headMediumProbabilityRandom VariablesView →
- Fox, goose, beans crossingMediumBrainteasersView →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- Grandmother's age from the digitsMediumBrainteasersView →
- Heads given the ends differMediumConditional Probability & ExpectationExpected ValueView →
- How fast the bubble's skin growsMediumCalculusView →
- Integrating arctangent by partsMediumCalculusView →
- Is W(t)³ a martingale?MediumStochastic ProcessesView →
- Keeping two apartMediumCombinatoricsView →
- Kelly sizing on an asymmetric betMediumMarket Making & Betting GamesView →
- Largest circle in a triangleMediumBrainteasersView →
- Lattice paths in 3DMediumCombinatoricsView →
- Letters into envelopesMediumProbabilityExpected ValueView →
- Log-dynamics of a geometric Brownian motionMediumStochastic ProcessesView →
- Matching floors of a logarithmMediumProbabilityRandom VariablesView →
- Mean over variance of a nested uniformMediumProbabilityRandom VariablesView →
- Median of a list and its squaresMediumCombinatoricsStatisticsView →
- Monotone paths across a gridMediumCombinatoricsView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- Multiplications in fast exponentiationMediumProgramming & DSAView →
- No face card before the two of heartsMediumProbabilityCombinatoricsView →
- No two evens adjacentMediumCombinatoricsView →
- No two neighboring bulbs litMediumProbabilityCombinatoricsView →
- Non-attacking rooksMediumCombinatoricsView →
- Odd multiples of threeMediumCombinatoricsBrainteasersView →
- Odd solutions to a sumMediumCombinatoricsView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- One hundred animals for a thousand dollarsMediumBrainteasersView →
- One random subset inside anotherMediumProbabilityCombinatoricsView →
- Order statistics of two uniformsMediumRandom VariablesStatisticsView →
- Placing operators among digitsMediumCombinatoricsView →
- Position of the first aceMediumConditional Probability & ExpectationExpected ValueView →
- Pricing a digital from a call spreadMediumFinance & DerivativesView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Put–call parity with a dividendMediumFinance & DerivativesView →
- Rank and nullity of a rotationMediumLinear AlgebraView →
- Ratio of partial sumsMediumRandom VariablesExpected ValueView →
- Rebuilding a tower of ten ringsMediumBrainteasersProgramming & DSAView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- Regions from ten linesMediumCombinatoricsBrainteasersView →
- Rolls to a six before a fiveMediumProbabilityExpected ValueView →
- Sampling an exponential from a uniformMediumRandom VariablesProgramming & DSAView →
- Simulate probability pMediumProbabilityProgramming & DSAView →
- Smallest simulable probabilityMediumProbabilityBrainteasersView →
- Sum of multinomial coefficientsMediumCombinatoricsView →
- Sum of the pandigital numbersMediumCombinatoricsBrainteasersView →
- Summing digits to a millionMediumCombinatoricsBrainteasersView →
- Ten dice, sum divisible by sixMediumProbabilityCombinatoricsView →
- Terms in a multinomial expansionMediumCombinatoricsView →
- The Gaussian integralMediumCalculusView →
- The SDE of the reciprocalMediumStochastic ProcessesView →
- The birthday problemMediumProbabilityCombinatoricsView →
- The die that makes sums uniformMediumProbabilityCombinatoricsView →
- The largest unmakeable totalMediumCombinatoricsBrainteasersView →
- The most balanced factorizationMediumBrainteasersView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- The two-headed coinMediumProbabilityConditional Probability & ExpectationView →
- Three ones in a rowMediumProbabilityCombinatoricsView →
- Three prisonersMediumProbabilityConditional Probability & ExpectationView →
- Three rolls, keep the lastMediumExpected ValueView →
- Three-four-five in Pascal's triangleMediumCombinatoricsBrainteasersView →
- Tiling a stripMediumCombinatoricsView →
- Trace of a productMediumLinear AlgebraView →
- Tuning an exponential random walkMediumProbabilityStochastic ProcessesView →
- Two childrenMediumProbabilityConditional Probability & ExpectationView →
- Two guards, two doorsMediumBrainteasersView →
- Two ropes, 45 minutesMediumBrainteasersView →
- Units digit of a random powerMediumProbabilityCombinatoricsView →
- Value of iⁱMediumCalculusView →
- Volume where two cylinders crossMediumCalculusView →
- When the naive shuffle is biasedMediumProgramming & DSAView →
- Width of a market under uncertaintyMediumMarket Making & Betting GamesStatisticsView →
- A 12 before two 7sHardProbabilityStochastic ProcessesView →
- A Fibonacci power sumHardBrainteasersView →
- A coin thick enough to land on its sideHardProbabilityBrainteasersView →
- A flea's shortest escape across a boxHardBrainteasersCalculusView →
- A geometric series that sums to a squareHardBrainteasersView →
- A rectangle over the shaded rowHardProbabilityCombinatoricsView →
- A second red ball from the same urnHardProbabilityConditional Probability & ExpectationView →
- A small sub-triangleHardProbabilityRandom VariablesView →
- A three-way race to the first headHardProbabilityRandom VariablesView →
- A triangle of consecutive integersHardBrainteasersView →
- A weighted sum of binomialsHardCombinatoricsBrainteasersView →
- Average of near-diagonal numbersHardCombinatoricsBrainteasersView →
- Balls into bowls, three eachHardCombinatoricsView →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Cats and miceHardBrainteasersView →
- Conditioning a Brownian bridgeHardStochastic ProcessesView →
- Counting fives before a four and a sixHardProbabilityRandom VariablesView →
- Cubes over the terminating denominatorsHardBrainteasersCalculusView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Dealing until kings or a king-and-aceHardCombinatoricsExpected ValueView →
- Digits with distinct pairwise sumsHardCombinatoricsBrainteasersView →
- Domino tilings of a 3×8 gridHardCombinatoricsView →
- Doors toggled by primesHardCombinatoricsBrainteasersView →
- Draws to beat a hidden uniformHardRandom VariablesExpected ValueView →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- Everyone gets one of eachHardProbabilityCombinatoricsView →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected chord between two random pointsHardProbabilityExpected ValueView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Expected local maxima in a shuffleHardProbabilityExpected ValueView →
- Filling three bins from a coin flipHardProbabilityCombinatoricsView →
- Guessing cards from a known pileHardProbabilityExpected ValueView →
- HTH before HHTHardProbabilityRandom VariablesView →
- Head density with no two in a rowHardProbabilityCombinatoricsView →
- Hitting zero on a ringHardProbabilityStochastic ProcessesView →
- How many long cycles?HardProbabilityCombinatoricsView →
- Laplace transform of a Brownian exit timeHardStochastic ProcessesView →
- Largest pairwise-coprime subset sumHardCombinatoricsBrainteasersView →
- Locks for a four-of-seven safeHardCombinatoricsBrainteasersView →
- Long cycles in a random permutationHardCombinatoricsExpected ValueView →
- Loops from tying noodlesHardProbabilityExpected ValueView →
- Making a power of Brownian motion a martingaleHardStochastic ProcessesView →
- Measuring two pintsHardBrainteasersView →
- More coins, more heads?HardProbabilityCombinatoricsView →
- No two samples too closeHardProbabilityCombinatoricsView →
- Odd sums on a 3×3 gridHardProbabilityCombinatoricsView →
- One of each face before the two of heartsHardProbabilityCombinatoricsView →
- Only seven left unchosenHardProbabilityCombinatoricsView →
- Overshoot past oneHardProbabilityRandom VariablesView →
- Pairing gloves within oneHardProbabilityCombinatoricsView →
- Pairing with a difference of 1 or 11HardCombinatoricsBrainteasersView →
- Pairs left in the drawerHardCombinatoricsExpected ValueView →
- Penalty kicks with a shifting rateHardProbabilityRandom VariablesView →
- Pirate gameHardMarket Making & Betting GamesView →
- Quadratic variation in mean-squareHardStochastic ProcessesView →
- Reading N(d₂) in Black–ScholesHardFinance & DerivativesView →
- Rolls to a six, given all evenHardConditional Probability & ExpectationExpected ValueView →
- Rotations divisible by 37HardCombinatoricsBrainteasersView →
- Runs of red and blue marblesHardCombinatoricsExpected ValueView →
- Second moment of a Gaussian-kernel stochastic integralHardCalculusStochastic ProcessesView →
- Seven seated in age orderHardProbabilityCombinatoricsView →
- Shortest of three piecesHardProbabilityRandom VariablesView →
- Shuffles to restore the deckHardCombinatoricsBrainteasersView →
- Six pieces, none past a halfHardProbabilityRandom VariablesView →
- Smallest card sharing a boxHardProbabilityExpected ValueView →
- Smallest number with digit product 10000HardCombinatoricsBrainteasersView →
- Smallest possible MGF valueHardRandom VariablesStatisticsView →
- Spread of a multinomial count gapHardRandom VariablesStatisticsView →
- Subsets with one consecutive pairHardCombinatoricsView →
- Sum of repeating decimalsHardCombinatoricsBrainteasersView →
- Sums of fours and fivesHardCombinatoricsBrainteasersView →
- Ten prime digits with a set productHardCombinatoricsView →
- The boy born on a TuesdayHardProbabilityConditional Probability & ExpectationView →
- The decreasing run of uniformsHardRandom VariablesExpected ValueView →
- The drunk passengerHardProbabilityConditional Probability & ExpectationView →
- The frog's single leftward hopHardProbabilityCombinatoricsView →
- The leap-frog's favorite landing spotHardProbabilityStochastic ProcessesView →
- The number with no new digitsHardBrainteasersView →
- The snow plowHardCalculusView →
- The survivor in the circleHardBrainteasersView →
- Three eggs, nine dropsHardCombinatoricsBrainteasersView →
- Three first-heads in non-decreasing orderHardProbabilityRandom VariablesView →
- Triangle with equal side sumsHardCombinatoricsBrainteasersView →
- Twelve balls, one oddHardBrainteasersView →
- Two random segments overlappingHardProbabilityRandom VariablesView →
- Two walks returning togetherHardProbabilityCombinatoricsView →
- Two-color necklacesHardCombinatoricsView →
- Uniforms summing past 1HardRandom VariablesExpected ValueView →
- Variance of an Itô integralHardStochastic ProcessesView →
- Weighings for the odd beanHardBrainteasersView →
- When a power of the process is a submartingaleHardProbabilityStochastic ProcessesView →
- When a uniform ratio rounds to a squareHardProbabilityRandom VariablesView →
- When k-to-the-k is a squareHardCombinatoricsBrainteasersView →
- When the extremes sum above oneHardProbabilityRandom VariablesView →
- Will the three-legged table stand?HardProbabilityView →
- Three children, all boysEasyProbabilityConditional Probability & Expectation Premium
- A convexity gap by JensenMediumRandom VariablesExpected Value Premium
- A divergent reciprocal expectationMediumRandom VariablesCalculus Premium
- A limit via the cosine seriesMediumCalculus Premium
- Adverse selection in quotingMediumMarket Making & Betting Games Premium
- An integral by symmetryMediumCalculus Premium
- Area of a parallelogramMediumLinear Algebra Premium
- Backing out the informed flow from imbalanceMediumMarket Making & Betting Games Premium
- Call count of memoized FibonacciMediumProgramming & DSA Premium
- Cash-and-carry arbitrage profitMediumFinance & Derivatives Premium
- Climbing stairsMediumCombinatoricsProgramming & DSA Premium
- CompositionsMediumCombinatorics Premium
- Convergence of the integral of x^(-p)MediumCalculus Premium
- Conversion arbitrage from a parity violationMediumFinance & Derivatives Premium
- Count set bitsMediumProgramming & DSA Premium
- Definite integral of x e^x on [0,1]MediumCalculus Premium
- Delta of a straddleMediumFinance & Derivatives Premium
- Double integral of x + y over the unit squareMediumCalculus Premium
- Equivalent continuously-compounded rateMediumFinance & Derivatives Premium
- Expectation of e raised to a normalMediumRandom VariablesExpected Value Premium
- Expected ascents in a shuffleMediumCombinatoricsExpected Value Premium
- Expected duration of a fair gameMediumExpected ValueStochastic Processes Premium
- Expected rolls for two sixes in a rowMediumExpected ValueStochastic Processes Premium
- Fair value after two informed buysMediumMarket Making & Betting Games Premium
- Gamma and rehedging P&LMediumFinance & Derivatives Premium
- HT before HH in coin flipsMediumProbabilityStochastic Processes Premium
- How many trials to poll a proportionMediumRandom VariablesStatistics Premium
- Implied dividend yield from a forwardMediumFinance & Derivatives Premium
- Integral by substitution: 2x e^(x^2)MediumCalculus Premium
- Inventory skewMediumMarket Making & Betting Games Premium
- Inversions in a shuffleMediumCombinatoricsExpected Value Premium
- Is the random walk squared a martingale?MediumExpected ValueStochastic Processes Premium
- Law of total varianceMediumConditional Probability & ExpectationExpected Value Premium
- Leibniz rule derivative at x = 1MediumCalculus Premium
- Limit of x^100 over e^xMediumCalculus Premium
- Marking a seasoned forwardMediumFinance & Derivatives Premium
- Markov with a floorMediumStatistics Premium
- Max rectangle under a parabolaMediumCalculus Premium
- Maximize x + y on the unit circleMediumLinear AlgebraCalculus Premium
- Median of a linear densityMediumRandom VariablesCalculus Premium
- Memoryless waitingMediumConditional Probability & ExpectationRandom Variables Premium
- Minimum given the maximumMediumProbabilityConditional Probability & Expectation Premium
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & Expectation Premium
- No two heads in a rowMediumProbabilityCombinatorics Premium
- No-arbitrage call boundsMediumFinance & Derivatives Premium
- Onto functionsMediumCombinatorics Premium
- Optimal bid-ask placementMediumMarket Making & Betting Games Premium
- Optimally pooling two estimatorsMediumRandom VariablesStatistics Premium
- Pair at a round tableMediumCombinatorics Premium
- Pairing up six peopleMediumCombinatorics Premium
- Paths on a 4×3 gridMediumCombinatorics Premium
- Periodicity and limiting distributionMediumStochastic Processes Premium
- Power of three in a factorialMediumCombinatorics Premium
- Reading order flowMediumMarket Making & Betting Games Premium
- Regression to the meanMediumBrainteasersStatistics Premium
- Remaining life of a memoryless partMediumRandom Variables Premium
- Risk-neutral up probabilityMediumStochastic ProcessesFinance & Derivatives Premium
- Rolls until a face repeatsMediumProbabilityExpected Value Premium
- Second-price auction strategyMediumProbabilityMarket Making & Betting Games Premium
- Short-straddle P&L when vol stays lowMediumFinance & Derivatives Premium
- Spaced onesMediumCombinatorics Premium
- The larger die shows a 4MediumProbabilityRandom Variables Premium
- The missing dollarMediumBrainteasers Premium
- The probability integral transformMediumRandom VariablesStatistics Premium
- The two black aces, side by sideMediumProbabilityCombinatorics Premium
- Three mislabeled jarsMediumBrainteasers Premium
- Three unlabeled teamsMediumCombinatorics Premium
- Two trains and a flyMediumBrainteasers Premium
- Variance of a stochastic integralMediumProbabilityStochastic Processes Premium
- Weighing 1 to 40MediumBrainteasers Premium
- When to prefer memoization over tabulationMediumProgramming & DSA Premium
- Which coin produced two heads?MediumProbabilityConditional Probability & Expectation Premium
- Wine and waterMediumBrainteasers Premium
- Winning from deuceMediumProbabilityConditional Probability & Expectation Premium
- Within distance d on the unit intervalMediumProbabilityCalculus Premium
- k-th order statisticMediumExpected ValueStatistics Premium
- A telescoping partial-fraction sumHardCalculus Premium
- A void suit in bridgeHardProbabilityCombinatorics Premium
- Ages from product and sumHardCombinatoricsBrainteasers Premium
- Amoeba extinctionHardProbabilityStochastic Processes Premium
- An arithmetic-geometric seriesHardCalculus Premium
- Bertrand's chordHardProbabilityBrainteasers Premium
- Best-of-seven underdogHardProbabilityRandom Variables Premium
- Blue-eyed islandersHardBrainteasers Premium
- Bluffing frequency in pokerHardProbabilityExpected Value Premium
- Branching process extinction (critical)HardProbabilityStochastic Processes Premium
- Broken-stick triangleHardProbability Premium
- Buffon's needleHardProbabilityCalculus Premium
- Connecting noodlesHardProbabilityExpected Value Premium
- Correlation of min and maxHardProbabilityRandom Variables Premium
- Counting two-pair handsHardProbabilityCombinatorics Premium
- Cycles in a shuffleHardCombinatoricsExpected Value Premium
- Defective stack of coinsHardCombinatoricsBrainteasers Premium
- Deriving the first-price shading factorHardProbabilityExpected Value Premium
- Draws until a smaller valueHardExpected Value Premium
- Drunk man on a bridgeHardExpected ValueStochastic Processes Premium
- Ehrenfest urn stationary distributionHardProbabilityStochastic Processes Premium
- Expected comparisons, from first principlesHardProgramming & DSA Premium
- Expected flips for HHHHardExpected ValueStochastic Processes Premium
- Expected flips for HTHHardExpected ValueStochastic Processes Premium
- Exponential martingale compensatorHardCalculusStochastic Processes Premium
- Four heads in a rowHardExpected ValueStochastic Processes Premium
- Handshakes at a dinner partyHardCombinatoricsBrainteasers Premium
- Hats in a lineHardBrainteasers Premium
- Hats with 100 colorsHardBrainteasers Premium
- Inverse via Cayley–HamiltonHardLinear Algebra Premium
- Laplace's rule of successionHardProbabilityConditional Probability & Expectation Premium
- Last one standingHardCombinatoricsBrainteasers Premium
- Making change in lineHardCombinatoricsStochastic Processes Premium
- Optional stopping between +3 and −5HardExpected ValueStochastic Processes Premium
- Prisoners and the boxesHardProbabilityBrainteasers Premium
- Prisoners and the light switchHardBrainteasers Premium
- Ratio of two normalsHardRandom VariablesStatistics Premium
- Reservoir samplingHardStatisticsProgramming & DSA Premium
- The all-pay auctionHardProbabilityExpected Value Premium
- The racing camelsHardBrainteasers Premium
- The two-envelopes paradoxHardProbabilityConditional Probability & Expectation Premium
- Triangle that swallows the centerHardProbabilityBrainteasers Premium
- Two Newton iterations for a square rootHardCalculusProgramming & DSA Premium
- Two coprime integersHardProbabilityCombinatorics Premium
- Two eggs, 100 floorsHardBrainteasers Premium
- World Series bettingHardExpected ValueStochastic Processes Premium
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Start practising freeFrequently asked questions
- What does a probability and market-making interview focus on?
- Probability, expected value, and fast mental math, often wrapped in betting-game and quoting scenarios. Interviewers care about clear reasoning under uncertainty as much as the final number.
- How should I prepare for this format?
- Build probability and EV fluency, practise thinking out loud, and get comfortable quoting and updating prices. Working a large, varied question set with worked solutions is the most reliable approach.
- Do I need a finance background?
- Usually not. These rounds test probabilistic reasoning and decision-making rather than finance vocabulary, so a background in maths, physics, CS, or engineering is a fine starting point.