Medium Trader Interview Questions
Everything asked of traders, filtered to the medium end - useful for calibrating where you actually are.
195 questions, 101 of them free to practise right now. The topics that come up most are probability (76), expected value (39), combinatorics (34), market making & betting games (31).
- 25 horses, 5 tracksMediumBrainteasersView →
- A 5 before a 7MediumProbabilityView →
- A low medianMediumProbabilityRandom VariablesView →
- A prime sum on prime diceMediumProbabilityCombinatoricsView →
- An ace for everyoneMediumProbabilityCombinatoricsView →
- An ace in every pileMediumProbabilityCombinatoricsView →
- Arbitraging a coupon bond against zerosMediumFinance & DerivativesView →
- Balancing six- and eight-sided diceMediumExpected ValueBrainteasersView →
- Bertrand's boxMediumProbabilityConditional Probability & ExpectationView →
- Boy–girl neighbors in a lineMediumCombinatoricsExpected ValueView →
- Bridge and torchMediumBrainteasersView →
- Capturing the spreadMediumMarket Making & Betting GamesView →
- Cash out or bustMediumProbabilityExpected ValueView →
- Cats and dogs on the streetMediumBrainteasersView →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Clock hands overlapMediumBrainteasersView →
- Coin sets the number of dice rollsMediumProbabilityConditional Probability & ExpectationView →
- Coin-pile NimMediumBrainteasersMarket Making & Betting GamesView →
- Cutting a cube into 27MediumBrainteasersView →
- Dice game, up to three rollsMediumExpected ValueStochastic ProcessesView →
- Dice payoff via WaldMediumExpected ValueStochastic ProcessesView →
- Distributing candies with a capMediumCombinatoricsView →
- Eight dice summing to twelveMediumProbabilityCombinatoricsView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- Exactly two aces in a bridge handMediumProbabilityCombinatoricsView →
- Expected fives before the first sixMediumProbabilityExpected ValueView →
- Expected flips for HHTMediumExpected ValueStochastic ProcessesView →
- Expected flips for HTMediumExpected ValueStochastic ProcessesView →
- Expected gap on 30-sided diceMediumProbabilityExpected ValueView →
- Expected maximum of two diceMediumRandom VariablesExpected ValueView →
- Expected median of three diceMediumProbabilityExpected ValueView →
- Expected value of the highest cardMediumProbabilityExpected ValueView →
- Filling a pool with the drain openMediumBrainteasersView →
- First HH on the tenth tossMediumProbabilityCombinatoricsView →
- First consecutive repeatMediumProbabilityExpected ValueView →
- First head on an even flipMediumProbabilityView →
- First head strictly soonerMediumProbabilityRandom VariablesView →
- First to three of a kind in a rowMediumProbabilityExpected ValueView →
- Four fives before the first sixMediumProbabilityRandom VariablesView →
- Four times as long to the first headMediumProbabilityRandom VariablesView →
- Fox, goose, beans crossingMediumBrainteasersView →
- Full housesMediumProbabilityCombinatoricsView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- Gamma-scalping a round tripMediumFinance & DerivativesView →
- Grandmother's age from the digitsMediumBrainteasersView →
- Guess 2/3 of the averageMediumMarket Making & Betting GamesView →
- Heads given the ends differMediumConditional Probability & ExpectationExpected ValueView →
- Implied vol from a straddle quoteMediumFinance & DerivativesView →
- Keeping two apartMediumCombinatoricsView →
- Kelly sizing on an asymmetric betMediumMarket Making & Betting GamesView →
- Largest circle in a triangleMediumBrainteasersView →
- Locking a profit by hedging after the odds moveMediumExpected ValueMarket Making & Betting GamesView →
- Matching penniesMediumMarket Making & Betting GamesView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- No face card before the two of heartsMediumProbabilityCombinatoricsView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- One hundred animals for a thousand dollarsMediumBrainteasersView →
- Pay to play with a capMediumExpected ValueMarket Making & Betting GamesView →
- Pricing a digital from a call spreadMediumFinance & DerivativesView →
- Pricing the higher of two diceMediumExpected ValueMarket Making & Betting GamesView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Product of two uniforms above a halfMediumProbabilityRandom VariablesView →
- Profit on a bull call spreadMediumFinance & DerivativesView →
- Profit on a risk reversalMediumFinance & DerivativesView →
- Put–call parity with a dividendMediumFinance & DerivativesView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- Rehedging a book after a moveMediumFinance & DerivativesView →
- Rolling a 5-sided die to reach fiveMediumProbabilityExpected ValueView →
- Rolling until two rolls differ by twoMediumProbabilityExpected ValueView →
- Rolls to a six before a fiveMediumProbabilityExpected ValueView →
- Russian roulette, re-spunMediumProbabilityConditional Probability & ExpectationView →
- Sharpe ratio in a marble gameMediumExpected ValueStatisticsView →
- Sizing a cross-book arbitrage lockMediumMarket Making & Betting GamesView →
- Sum of multiples of 3 or 5MediumBrainteasersView →
- Sum versus twice the differenceMediumProbabilityRandom VariablesView →
- Tennis: two sets or three?MediumProbabilityView →
- The birthday problemMediumProbabilityCombinatoricsView →
- The bridge crossingMediumBrainteasersView →
- The largest unmakeable totalMediumCombinatoricsBrainteasersView →
- The last lightbulb to burn outMediumRandom VariablesExpected ValueView →
- The profitable range of a short strangleMediumFinance & DerivativesView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- The third shiny pennyMediumProbabilityCombinatoricsView →
- The two-headed coinMediumProbabilityConditional Probability & ExpectationView →
- Three dots on a squareMediumProbabilityCombinatoricsView →
- Three ones in a rowMediumProbabilityCombinatoricsView →
- Three prisonersMediumProbabilityConditional Probability & ExpectationView →
- Three rolls, keep the lastMediumExpected ValueView →
- Three-jug measuringMediumBrainteasersView →
- Two childrenMediumProbabilityConditional Probability & ExpectationView →
- Two guards, two doorsMediumBrainteasersView →
- Two ropes, 45 minutesMediumBrainteasersView →
- Variance of a coin-gated payoffMediumRandom VariablesStatisticsView →
- Variance of the longer pieceMediumProbabilityRandom VariablesView →
- Waiting to see both facesMediumRandom VariablesStatisticsView →
- When time decay reversesMediumFinance & DerivativesView →
- Which deck for two reds?MediumProbabilityView →
- Width of a market under uncertaintyMediumMarket Making & Betting GamesStatisticsView →
- Winner's curseMediumMarket Making & Betting GamesView →
- A convexity gap by JensenMediumRandom VariablesExpected Value Premium
- A cube root by tangent lineMediumCalculus Premium
- Absorption probability on a lineMediumProbabilityStochastic Processes Premium
- Aces in a seven-card handMediumCombinatoricsExpected Value Premium
- Adverse selection in quotingMediumMarket Making & Betting Games Premium
- An ace in the handMediumProbabilityCombinatorics Premium
- Ants on a stickMediumBrainteasers Premium
- Arbitraging a mispriced forward loanMediumFinance & Derivatives Premium
- At least two sixes in five rollsMediumProbabilityRandom Variables Premium
- Backing out a correlationMediumRandom VariablesStatistics Premium
- Backing out a margin-free probabilityMediumMarket Making & Betting Games Premium
- Backing out the informed flow from imbalanceMediumMarket Making & Betting Games Premium
- Balloon related ratesMediumCalculus Premium
- Both even given an even sumMediumProbabilityConditional Probability & Expectation Premium
- Break-even fill quality for a resting bidMediumMarket Making & Betting Games Premium
- Break-even half-spread from toxic flowMediumProbabilityExpected Value Premium
- Break-even half-spread under adverse selectionMediumExpected ValueMarket Making & Betting Games Premium
- Buyer count in a thinned arrival streamMediumProbabilityStochastic Processes Premium
- Calendar spread intuitionMediumFinance & Derivatives Premium
- Cash-and-carry arbitrageMediumFinance & Derivatives Premium
- Cash-and-carry arbitrage profitMediumFinance & Derivatives Premium
- Conversion arbitrage from a parity violationMediumFinance & Derivatives Premium
- Correlation of overlapping sumsMediumRandom VariablesStatistics Premium
- Counting straightsMediumProbabilityCombinatorics Premium
- Cutting a cubeMediumBrainteasers Premium
- Delta of a straddleMediumFinance & Derivatives Premium
- Delta-hedge a two-leg option bookMediumFinance & Derivatives Premium
- Eight coins, one lightMediumCombinatoricsBrainteasers Premium
- Expected absolute difference of two diceMediumExpected Value Premium
- Expected maximum of three diceMediumRandom VariablesExpected Value Premium
- Expected minimum of two diceMediumRandom VariablesExpected Value Premium
- Expected revenue of a Vickrey auctionMediumProbabilityExpected Value Premium
- Fair price of a die with one re-rollMediumExpected ValueMarket Making & Betting Games Premium
- Fair value after an informed buyMediumConditional Probability & ExpectationMarket Making & Betting Games Premium
- Fair value after two informed buysMediumMarket Making & Betting Games Premium
- First to roll a sixMediumProbability Premium
- Five distinct ranksMediumProbabilityCombinatorics Premium
- Forward vs. futures priceMediumFinance & Derivatives Premium
- Four distinct birth monthsMediumProbabilityCombinatorics Premium
- Frog in the wellMediumBrainteasers Premium
- Gamma and rehedging P&LMediumFinance & Derivatives Premium
- HT before HH in coin flipsMediumProbabilityStochastic Processes Premium
- Implied dividend yield from a forwardMediumFinance & Derivatives Premium
- Inventory skewMediumMarket Making & Betting Games Premium
- Inventory-skewed reservation priceMediumMarket Making & Betting Games Premium
- Large sum given a sixMediumProbabilityConditional Probability & Expectation Premium
- Limit of x ln x as x to 0+MediumCalculus Premium
- Limit of x^100 over e^xMediumCalculus Premium
- MLE at a boundaryMediumStatisticsCalculus Premium
- Marking a seasoned forwardMediumFinance & Derivatives Premium
- Maximum loss on a collarMediumFinance & Derivatives Premium
- Minimum defense frequency against a betMediumProbabilityExpected Value Premium
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & Expectation Premium
- Neither die exceeds fourMediumProbabilityRandom Variables Premium
- No-arbitrage call boundsMediumFinance & Derivatives Premium
- Optimal bid-ask placementMediumMarket Making & Betting Games Premium
- Optimal quote widthMediumMarket Making & Betting Games Premium
- Pair at a round tableMediumCombinatorics Premium
- Paths dodging a closed intersectionMediumCombinatorics Premium
- Position of the first spadeMediumCombinatoricsExpected Value Premium
- Pricing a coupon bond off the spot curveMediumFinance & Derivatives Premium
- Pricing a squared payoffMediumExpected ValueMarket Making & Betting Games Premium
- Prime sumMediumProbability Premium
- Put–call parity arbitrageMediumFinance & Derivatives Premium
- Rare-event Poisson approximationMediumProbabilityRandom Variables Premium
- Reaching the target before ruinMediumStochastic Processes Premium
- Reading order flowMediumMarket Making & Betting Games Premium
- Right angles in 12 hoursMediumBrainteasers Premium
- Risk-neutral up probabilityMediumStochastic ProcessesFinance & Derivatives Premium
- Rolls to see both a 1 and a 2MediumExpected Value Premium
- Scaling vega across maturitiesMediumFinance & Derivatives Premium
- Second-price auction strategyMediumProbabilityMarket Making & Betting Games Premium
- Short-straddle P&L when vol stays lowMediumFinance & Derivatives Premium
- Sum of 10 with three diceMediumProbabilityCombinatorics Premium
- The St. Petersburg paradoxMediumExpected ValueMarket Making & Betting Games Premium
- The gold chainMediumBrainteasers Premium
- The larger die shows a 4MediumProbabilityRandom Variables Premium
- The missing dollarMediumBrainteasers Premium
- The pile that always leaves oneMediumBrainteasers Premium
- The winner's curse in a bid warMediumMarket Making & Betting Games Premium
- Three mislabeled jarsMediumBrainteasers Premium
- Two face cardsMediumProbabilityCombinatorics Premium
- Two reds in a row from a shrinking urnMediumProbabilityConditional Probability & Expectation Premium
- Two trains and a flyMediumBrainteasers Premium
- Two uniforms summing below a halfMediumProbabilityRandom Variables Premium
- Two uniforms summing past 1.5MediumProbabilityCalculus Premium
- Two-sided p-value of a mean testMediumStatistics Premium
- Volatility smile meaningMediumStatisticsFinance & Derivatives Premium
- Weighing 1 to 40MediumBrainteasers Premium
- Which coin produced two heads?MediumProbabilityConditional Probability & Expectation Premium
- Which desk books the larger dayMediumRandom VariablesStatistics Premium
- Wine and waterMediumBrainteasers Premium
- Winning from deuceMediumProbabilityConditional Probability & Expectation Premium
- Within distance d on the unit intervalMediumProbabilityCalculus Premium
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