Probability Questions for Market Maker Interviews
A market maker round does not test probability the way a textbook does. This set is the overlap - the probability questions that actually turn up in this format.
141 questions, all free to practise. The split is 21 easy, 55 medium, 65 hard.
- A divisor of a power of tenEasyProbabilityCombinatoricsView →
- A specific sequence given three headsEasyProbabilityConditional Probability & ExpectationView →
- All four aces before any kingEasyProbabilityCombinatoricsView →
- Beating a product of uniformsEasyProbabilityRandom VariablesView →
- Beating three othersEasyProbabilityRandom VariablesView →
- Correlation of two event indicatorsEasyProbabilityStatisticsView →
- Even heads with one fair coinEasyProbabilityConditional Probability & ExpectationView →
- Expected flips for two heads (not in a row)EasyProbabilityExpected ValueView →
- Keep it or draw againEasyProbabilityExpected ValueView →
- Matching a max and a min at zeroEasyProbabilityView →
- More heads than tails in six flipsEasyProbabilityView →
- Reflipping for valueEasyProbabilityExpected ValueView →
- The added babyEasyProbabilityConditional Probability & ExpectationView →
- The top two cards form a pairEasyProbabilityCombinatoricsView →
- Three children, all boysEasyProbabilityConditional Probability & ExpectationView →
- Three cube faces at a cornerEasyProbabilityCombinatoricsView →
- Two primes with an even sumEasyProbabilityCombinatoricsView →
- Unchanged after ten swingsEasyProbabilityBrainteasersView →
- Units digit of a random productEasyProbabilityCombinatoricsView →
- Where the arrivals landEasyProbabilityStochastic ProcessesView →
- Whether either bus comes soonEasyProbabilityRandom VariablesView →
- 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 →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Coin sets the number of dice rollsMediumProbabilityConditional Probability & ExpectationView →
- Cosine of a conditional meanMediumProbabilityConditional Probability & ExpectationView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- Exactly two aces in a bridge handMediumProbabilityCombinatoricsView →
- Expected fives before the first sixMediumProbabilityExpected ValueView →
- Fair outcome from a biased coinMediumProbabilityStatisticsView →
- First HH on the tenth tossMediumProbabilityCombinatoricsView →
- 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 →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- HT before HH in coin flipsMediumProbabilityStochastic ProcessesView →
- Letters into envelopesMediumProbabilityExpected ValueView →
- Matching floors of a logarithmMediumProbabilityRandom VariablesView →
- Mean over variance of a nested uniformMediumProbabilityRandom VariablesView →
- Minimum given the maximumMediumProbabilityConditional Probability & ExpectationView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & ExpectationView →
- 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 →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Rolls to a six before a fiveMediumProbabilityExpected ValueView →
- Rolls until a face repeatsMediumProbabilityExpected ValueView →
- Second-price auction strategyMediumProbabilityMarket Making & Betting GamesView →
- Simulate probability pMediumProbabilityProgramming & DSAView →
- Smallest simulable probabilityMediumProbabilityBrainteasersView →
- Ten dice, sum divisible by sixMediumProbabilityCombinatoricsView →
- The birthday problemMediumProbabilityCombinatoricsView →
- The die that makes sums uniformMediumProbabilityCombinatoricsView →
- The larger die shows a 4 - what about the smaller?MediumProbabilityRandom VariablesView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- The two black aces, side by sideMediumProbabilityCombinatoricsView →
- The two-headed coinMediumProbabilityConditional Probability & ExpectationView →
- 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 a stochastic integralMediumProbabilityStochastic ProcessesView →
- Which coin produced two heads?MediumProbabilityConditional Probability & ExpectationView →
- Winning from deuceMediumProbabilityConditional Probability & ExpectationView →
- Within distance d on the unit intervalMediumProbabilityCalculusView →
- A 12 before two 7sHardProbabilityStochastic ProcessesView →
- A coin thick enough to land on its sideHardProbabilityBrainteasersView →
- 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 →
- Bluffing frequency in pokerHardProbabilityExpected ValueView →
- Branching process extinction (critical)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 →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- Ehrenfest urn stationary distributionHardProbabilityStochastic ProcessesView →
- 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 →
- 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 →
- 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 two-envelopes paradoxHardProbabilityConditional Probability & ExpectationView →
- Three first-heads in non-decreasing orderHardProbabilityRandom VariablesView →
- Triangle that swallows the centerHardProbabilityBrainteasersView →
- Two coprime integersHardProbabilityCombinatoricsView →
- Two elements in the long cycleHardProbabilityCombinatoricsView →
- Two random segments overlappingHardProbabilityRandom VariablesView →
- 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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