Hard Probability Interview Questions
These are the probability questions that separate candidates who know the technique from those who can apply it under pressure.
77 questions, 54 of them free to practise right now.
- 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 →
- A void suit in bridgeHardProbabilityCombinatorics Premium
- Amoeba extinctionHardProbabilityStochastic Processes Premium
- Bertrand's chordHardProbabilityBrainteasers Premium
- Best-of-seven underdogHardProbabilityRandom Variables Premium
- Bluffing frequency in pokerHardProbabilityExpected Value 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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