Probability Interview Questions for Quant Researchers
Quant Researchers get asked probability differently from other quant roles - the emphasis shifts with what the job actually does. This is that slice.
238 questions, all free to practise. The split is 58 easy, 104 medium, 76 hard.
- A die with one face decrementedEasyProbabilityConditional Probability & ExpectationView →
- A divisor of a power of tenEasyProbabilityCombinatoricsView →
- A specific sequence given three headsEasyProbabilityConditional Probability & ExpectationView →
- A sum of four before a sum of twoEasyProbabilityView →
- All four aces before any kingEasyProbabilityCombinatoricsView →
- At least one blue and one greenEasyProbabilityCombinatoricsView →
- Beating a product of uniformsEasyProbabilityRandom VariablesView →
- Beating three othersEasyProbabilityRandom VariablesView →
- Correlation of two event indicatorsEasyProbabilityStatisticsView →
- Counting flushesEasyProbabilityCombinatoricsView →
- Determinant after antisymmetrizingEasyProbabilityLinear AlgebraView →
- Dots on distinct edgesEasyProbabilityCombinatoricsView →
- Even count until the coin repeatsEasyProbabilityView →
- Even heads with one fair coinEasyProbabilityConditional Probability & ExpectationView →
- Even-size, non-empty subsetEasyProbabilityCombinatoricsView →
- Exactly one clears two-thirdsEasyProbabilityRandom VariablesView →
- Expected distance of a dart from centerEasyProbabilityRandom VariablesView →
- Expected flips after a losing startEasyProbabilityExpected ValueView →
- Expected flips for three headsEasyProbabilityExpected ValueView →
- Expected flips for two heads (not in a row)EasyProbabilityExpected ValueView →
- Finding the number of blue socksEasyProbabilityCombinatoricsView →
- First tail within two flipsEasyProbabilityView →
- Four dice summing to twentyEasyProbabilityCombinatoricsView →
- Keep it or draw againEasyProbabilityExpected ValueView →
- Keep the d8 or gamble on the d12?EasyProbabilityExpected ValueView →
- Matching a max and a min at zeroEasyProbabilityView →
- Maximum of four uniforms in a bandEasyProbabilityRandom VariablesView →
- More heads than tails in six flipsEasyProbabilityView →
- No heads in a random number of flipsEasyProbabilityRandom VariablesView →
- One blue die matches the redEasyProbabilityView →
- Origin between two pointsEasyProbabilityView →
- Paid the last roll before you stopEasyProbabilityExpected ValueView →
- Reflipping for valueEasyProbabilityExpected ValueView →
- Rolling until you match the first rollEasyProbabilityExpected ValueView →
- Rolls until an even sumEasyProbabilityExpected ValueView →
- Same side four timesEasyProbabilityView →
- Sharing your weekday of birthEasyProbabilityView →
- The added babyEasyProbabilityConditional Probability & ExpectationView →
- The higher die shows a fourEasyProbabilityView →
- The top two cards form a pairEasyProbabilityCombinatoricsView →
- Three children, all boysEasyProbabilityConditional Probability & ExpectationView →
- Three cube faces at a cornerEasyProbabilityCombinatoricsView →
- Three distinct dice, no sixEasyProbabilityCombinatoricsView →
- Three primes in six rollsEasyProbabilityView →
- Top three dice summing to eighteenEasyProbabilityCombinatoricsView →
- Two heads given an even countEasyProbabilityConditional Probability & ExpectationView →
- Two mismatched diceEasyProbabilityView →
- Two numbers in different groupsEasyProbabilityCombinatoricsView →
- Two ordering constraints at onceEasyProbabilityCombinatoricsView →
- Two primes with an even sumEasyProbabilityCombinatoricsView →
- Unchanged after ten swingsEasyProbabilityBrainteasersView →
- Units digit of a random productEasyProbabilityCombinatoricsView →
- Upper bound on a dry weekendEasyProbabilityView →
- Ways to reach deuceEasyProbabilityCombinatoricsView →
- Where the arrivals landEasyProbabilityStochastic ProcessesView →
- Whether either bus comes soonEasyProbabilityRandom VariablesView →
- Which side holds the heavy weightEasyProbabilityCombinatoricsView →
- Winning by a growing marginEasyProbabilityBrainteasersView →
- A cube ending in elevenMediumProbabilityBrainteasersView →
- A low medianMediumProbabilityRandom VariablesView →
- A point near the cone's baseMediumProbabilityCalculusView →
- A prime sum on prime diceMediumProbabilityCombinatoricsView →
- Absorption probability on a lineMediumProbabilityStochastic ProcessesView →
- An ace for everyoneMediumProbabilityCombinatoricsView →
- An ace in every pileMediumProbabilityCombinatoricsView →
- An ace in the handMediumProbabilityCombinatoricsView →
- Arrivals before the rival streamMediumProbabilityStochastic ProcessesView →
- At least two sixes in five rollsMediumProbabilityRandom VariablesView →
- Bertrand's boxMediumProbabilityConditional Probability & ExpectationView →
- Buyer count in a thinned arrival streamMediumProbabilityStochastic ProcessesView →
- Cash out or bustMediumProbabilityExpected ValueView →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Coin sets the number of dice rollsMediumProbabilityConditional Probability & ExpectationView →
- Correlation of two face-countsMediumProbabilityStatisticsView →
- Cosine of a conditional meanMediumProbabilityConditional Probability & ExpectationView →
- Counting straightsMediumProbabilityCombinatoricsView →
- Density of a sum of two uniformsMediumProbabilityRandom VariablesView →
- Distinct birthdays representedMediumProbabilityExpected ValueView →
- Eight dice summing to twelveMediumProbabilityCombinatoricsView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- Exactly two aces in a bridge handMediumProbabilityCombinatoricsView →
- Expected fives before the first sixMediumProbabilityExpected ValueView →
- Expected gap on 30-sided diceMediumProbabilityExpected ValueView →
- Expected median of three diceMediumProbabilityExpected ValueView →
- Expected square of a random unit complex numberMediumProbabilityRandom VariablesView →
- Expected steps to first reach a levelMediumProbabilityStochastic ProcessesView →
- Expected value of the highest cardMediumProbabilityExpected ValueView →
- Fair outcome from a biased coinMediumProbabilityStatisticsView →
- First HH on the tenth tossMediumProbabilityCombinatoricsView →
- First consecutive repeatMediumProbabilityExpected ValueView →
- First head on an even flipMediumProbabilityView →
- First head strictly soonerMediumProbabilityRandom VariablesView →
- First to roll a sixMediumProbabilityView →
- First to three of a kind in a rowMediumProbabilityExpected ValueView →
- Five distinct ranksMediumProbabilityCombinatoricsView →
- Four fives before the first sixMediumProbabilityRandom VariablesView →
- Four points on a semicircleMediumProbabilityView →
- Four times as long to the first headMediumProbabilityRandom VariablesView →
- Fourth moment of a shifted normalMediumProbabilityRandom VariablesView →
- Full housesMediumProbabilityCombinatoricsView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- HT before HH in coin flipsMediumProbabilityStochastic ProcessesView →
- Joint default rangeMediumProbabilityFinance & DerivativesView →
- Letters into envelopesMediumProbabilityExpected ValueView →
- Matching floors of a logarithmMediumProbabilityRandom VariablesView →
- Mean over variance of a nested uniformMediumProbabilityRandom VariablesView →
- Minimum given the maximumMediumProbabilityConditional Probability & ExpectationView →
- Minimum of two exponentialsMediumProbabilityRandom VariablesView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & ExpectationView →
- Neither die exceeds fourMediumProbabilityRandom VariablesView →
- No face card before the two of heartsMediumProbabilityCombinatoricsView →
- No two heads in a rowMediumProbabilityCombinatoricsView →
- No two neighboring bulbs litMediumProbabilityCombinatoricsView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- One random subset inside anotherMediumProbabilityCombinatoricsView →
- Painted cube, one face showingMediumProbabilityBrainteasersView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Product of two uniforms above a halfMediumProbabilityRandom VariablesView →
- Rare-event Poisson approximationMediumProbabilityRandom VariablesView →
- 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 →
- Rolls until a face repeatsMediumProbabilityExpected ValueView →
- Russian roulette, re-spunMediumProbabilityConditional Probability & ExpectationView →
- Simulate probability pMediumProbabilityProgramming & DSAView →
- Smallest simulable probabilityMediumProbabilityBrainteasersView →
- Spam filterMediumProbabilityConditional Probability & ExpectationView →
- Stationary distribution of a two-state chainMediumProbabilityStochastic ProcessesView →
- Sum of 10 with three diceMediumProbabilityCombinatoricsView →
- Sum of independent PoissonsMediumProbabilityRandom VariablesView →
- Sum versus twice the differenceMediumProbabilityRandom VariablesView →
- Ten dice, sum divisible by sixMediumProbabilityCombinatoricsView →
- The birthday problemMediumProbabilityCombinatoricsView →
- The cab problemMediumProbabilityConditional Probability & ExpectationView →
- The die that makes sums uniformMediumProbabilityCombinatoricsView →
- The larger die shows a 4 - what about the smaller?MediumProbabilityRandom VariablesView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- The third shiny pennyMediumProbabilityCombinatoricsView →
- The two black aces, side by sideMediumProbabilityCombinatoricsView →
- The two-headed coinMediumProbabilityConditional Probability & ExpectationView →
- Three dots, exactly one shared edgeMediumProbabilityCombinatoricsView →
- Three ones in a rowMediumProbabilityCombinatoricsView →
- Three prisonersMediumProbabilityConditional Probability & ExpectationView →
- Tuning an exponential random walkMediumProbabilityStochastic ProcessesView →
- Two childrenMediumProbabilityConditional Probability & ExpectationView →
- Two positive testsMediumProbabilityConditional Probability & ExpectationView →
- Two uniforms summing below a halfMediumProbabilityRandom VariablesView →
- Two uniforms summing past 1.5MediumProbabilityCalculusView →
- Units digit of a random powerMediumProbabilityCombinatoricsView →
- Variance of a stochastic integralMediumProbabilityStochastic ProcessesView →
- Variance of the longer pieceMediumProbabilityRandom VariablesView →
- Variance-minimizing hedgeMediumProbabilityStatisticsView →
- Which coin produced two heads?MediumProbabilityConditional Probability & ExpectationView →
- Which deck for two reds?MediumProbabilityView →
- Whose draw is larger?MediumProbabilityView →
- Will they meet?MediumProbabilityView →
- Winning from deuceMediumProbabilityConditional Probability & ExpectationView →
- Within distance d on the unit intervalMediumProbabilityCalculusView →
- X positive given the sum is positiveMediumProbabilityRandom VariablesView →
- A 12 before two 7sHardProbabilityStochastic ProcessesView →
- A coin thick enough to land on its sideHardProbabilityBrainteasersView →
- A half-plane, given positiveHardProbabilityRandom VariablesView →
- 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 void suit in bridgeHardProbabilityCombinatoricsView →
- Amoeba extinctionHardProbabilityStochastic ProcessesView →
- Bertrand's chordHardProbabilityBrainteasersView →
- Best-of-seven underdogHardProbabilityRandom VariablesView →
- Branching process extinction (critical)HardProbabilityStochastic ProcessesView →
- Branching process extinction (supercritical)HardProbabilityStochastic ProcessesView →
- Broken-stick triangleHardProbabilityView →
- Buffon's needleHardProbabilityCalculusView →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Connecting noodlesHardProbabilityExpected ValueView →
- Correlation of min and maxHardProbabilityRandom VariablesView →
- Counting fives before a four and a sixHardProbabilityRandom VariablesView →
- Counting two-pair handsHardProbabilityCombinatoricsView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Deriving the first-price shading factorHardProbabilityExpected ValueView →
- Distinct toys from seven boxesHardProbabilityExpected ValueView →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- Ehrenfest urn stationary distributionHardProbabilityStochastic ProcessesView →
- Everyone gets one of eachHardProbabilityCombinatoricsView →
- Exactly one pairHardProbabilityCombinatoricsView →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected chord between two random pointsHardProbabilityExpected ValueView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- 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 →
- Laplace's rule of successionHardProbabilityConditional Probability & ExpectationView →
- Loops from tying noodlesHardProbabilityExpected ValueView →
- 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 →
- Penalty kicks with a shifting rateHardProbabilityRandom VariablesView →
- Prisoners and the boxesHardProbabilityBrainteasersView →
- Range beats the midpointHardProbabilityRandom VariablesView →
- Reflected paths ending below the levelHardProbabilityStochastic ProcessesView →
- Rolling until two rolls are closeHardProbabilityExpected ValueView →
- Rounds to see all faces with two diceHardProbabilityExpected ValueView →
- Seven seated in age orderHardProbabilityCombinatoricsView →
- Shortest of three piecesHardProbabilityRandom VariablesView →
- Six pieces, none past a halfHardProbabilityRandom VariablesView →
- Smallest card sharing a boxHardProbabilityExpected ValueView →
- The all-pay auctionHardProbabilityExpected ValueView →
- The boy born on a TuesdayHardProbabilityConditional Probability & ExpectationView →
- The drunk passengerHardProbabilityConditional Probability & ExpectationView →
- The frog's single leftward hopHardProbabilityCombinatoricsView →
- The leap-frog's favorite landing spotHardProbabilityStochastic ProcessesView →
- The reroll advantage in a die duelHardProbabilityMarket Making & Betting GamesView →
- The two-envelopes paradoxHardProbabilityConditional Probability & ExpectationView →
- Three first-heads in non-decreasing orderHardProbabilityRandom VariablesView →
- Triangle from three independent sticksHardProbabilityCalculusView →
- Triangle that swallows the centerHardProbabilityBrainteasersView →
- Two Brownian values, both positiveHardProbabilityStochastic ProcessesView →
- Two coprime integersHardProbabilityCombinatoricsView →
- Two elements in the long cycleHardProbabilityCombinatoricsView →
- Two random segments overlappingHardProbabilityRandom VariablesView →
- Two random subsets that overlapHardProbabilityCombinatoricsView →
- Two walks returning togetherHardProbabilityCombinatoricsView →
- When a power of the process is a submartingaleHardProbabilityStochastic ProcessesView →
- When a uniform ratio rounds to a squareHardProbabilityRandom VariablesView →
- When the extremes sum above oneHardProbabilityRandom VariablesView →
- Will the three-legged table stand?HardProbabilityView →
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