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.
237 questions, 180 of them free to practise right now. The split is 58 easy, 103 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 in a rowEasyProbabilityExpected 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 cube faces at a cornerEasyProbabilityCombinatoricsView →
- Three distinct dice, no sixEasyProbabilityCombinatoricsView →
- Three primes in six rollsEasyProbabilityView →
- Top three dice summing to eighteenEasyProbabilityCombinatoricsView →
- 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 →
- An ace for everyoneMediumProbabilityCombinatoricsView →
- An ace in every pileMediumProbabilityCombinatoricsView →
- Bertrand's boxMediumProbabilityConditional Probability & ExpectationView →
- 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 →
- Density of a sum of two uniformsMediumProbabilityRandom VariablesView →
- 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 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 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 →
- Full housesMediumProbabilityCombinatoricsView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- Letters into envelopesMediumProbabilityExpected ValueView →
- Matching floors of a logarithmMediumProbabilityRandom VariablesView →
- Mean over variance of a nested uniformMediumProbabilityRandom VariablesView →
- Minimum of two exponentialsMediumProbabilityRandom VariablesView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- No face card before the two of heartsMediumProbabilityCombinatoricsView →
- No two neighboring bulbs litMediumProbabilityCombinatoricsView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- One random subset inside anotherMediumProbabilityCombinatoricsView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Product of two uniforms above a halfMediumProbabilityRandom 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 →
- Russian roulette, re-spunMediumProbabilityConditional Probability & ExpectationView →
- Simulate probability pMediumProbabilityProgramming & DSAView →
- Smallest simulable probabilityMediumProbabilityBrainteasersView →
- Sum of independent PoissonsMediumProbabilityRandom VariablesView →
- Sum versus twice the differenceMediumProbabilityRandom VariablesView →
- Ten dice, sum divisible by sixMediumProbabilityCombinatoricsView →
- The birthday problemMediumProbabilityCombinatoricsView →
- The die that makes sums uniformMediumProbabilityCombinatoricsView →
- 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 →
- Tuning an exponential random walkMediumProbabilityStochastic ProcessesView →
- Two childrenMediumProbabilityConditional Probability & ExpectationView →
- Units digit of a random powerMediumProbabilityCombinatoricsView →
- Variance of the longer pieceMediumProbabilityRandom VariablesView →
- Which deck for two reds?MediumProbabilityView →
- Whose draw is larger?MediumProbabilityView →
- Will they meet?MediumProbabilityView →
- 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 →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Counting fives before a four and a sixHardProbabilityRandom VariablesView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Distinct toys from seven boxesHardProbabilityExpected 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 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 →
- 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 →
- Range beats the midpointHardProbabilityRandom VariablesView →
- 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 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 →
- Three first-heads in non-decreasing orderHardProbabilityRandom VariablesView →
- Two Brownian values, both positiveHardProbabilityStochastic ProcessesView →
- 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 →
- Three children, all boysEasyProbabilityConditional Probability & Expectation Premium
- Two heads given an even countEasyProbabilityConditional Probability & Expectation Premium
- Absorption probability on a lineMediumProbabilityStochastic Processes Premium
- An ace in the handMediumProbabilityCombinatorics Premium
- Arrivals before the rival streamMediumProbabilityStochastic Processes Premium
- At least two sixes in five rollsMediumProbabilityRandom Variables Premium
- Buyer count in a thinned arrival streamMediumProbabilityStochastic Processes Premium
- Counting straightsMediumProbabilityCombinatorics Premium
- Distinct birthdays representedMediumProbabilityExpected Value Premium
- Expected steps to first reach a levelMediumProbabilityStochastic Processes Premium
- First to roll a sixMediumProbability Premium
- Five distinct ranksMediumProbabilityCombinatorics Premium
- Fourth moment of a shifted normalMediumProbabilityRandom Variables Premium
- HT before HH in coin flipsMediumProbabilityStochastic Processes Premium
- Joint default rangeMediumProbabilityFinance & Derivatives Premium
- Minimum given the maximumMediumProbabilityConditional Probability & Expectation Premium
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & Expectation Premium
- Neither die exceeds fourMediumProbabilityRandom Variables Premium
- No two heads in a rowMediumProbabilityCombinatorics Premium
- Rare-event Poisson approximationMediumProbabilityRandom Variables Premium
- Rolls until a face repeatsMediumProbabilityExpected Value Premium
- Spam filterMediumProbabilityConditional Probability & Expectation Premium
- Stationary distribution of a two-state chainMediumProbabilityStochastic Processes Premium
- Sum of 10 with three diceMediumProbabilityCombinatorics Premium
- The cab problemMediumProbabilityConditional Probability & Expectation Premium
- The larger die shows a 4MediumProbabilityRandom Variables Premium
- The two black aces, side by sideMediumProbabilityCombinatorics Premium
- Two positive testsMediumProbabilityConditional Probability & Expectation Premium
- Two uniforms summing below a halfMediumProbabilityRandom Variables Premium
- Two uniforms summing past 1.5MediumProbabilityCalculus Premium
- Variance of a stochastic integralMediumProbabilityStochastic Processes Premium
- Variance-minimizing hedgeMediumProbabilityStatistics Premium
- Which coin produced two heads?MediumProbabilityConditional Probability & Expectation Premium
- Winning from deuceMediumProbabilityConditional Probability & Expectation Premium
- Within distance d on the unit intervalMediumProbabilityCalculus Premium
- A void suit in bridgeHardProbabilityCombinatorics Premium
- Amoeba extinctionHardProbabilityStochastic Processes Premium
- Bertrand's chordHardProbabilityBrainteasers Premium
- Best-of-seven underdogHardProbabilityRandom Variables Premium
- Branching process extinction (critical)HardProbabilityStochastic Processes Premium
- Branching process extinction (supercritical)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
- Deriving the first-price shading factorHardProbabilityExpected Value Premium
- Ehrenfest urn stationary distributionHardProbabilityStochastic Processes Premium
- Exactly one pairHardProbabilityCombinatorics Premium
- Laplace's rule of successionHardProbabilityConditional Probability & Expectation Premium
- Prisoners and the boxesHardProbabilityBrainteasers Premium
- Reflected paths ending below the levelHardProbabilityStochastic Processes Premium
- The all-pay auctionHardProbabilityExpected Value Premium
- The two-envelopes paradoxHardProbabilityConditional Probability & Expectation Premium
- Triangle from three independent sticksHardProbabilityCalculus Premium
- Triangle that swallows the centerHardProbabilityBrainteasers Premium
- Two coprime integersHardProbabilityCombinatorics Premium
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