Expected Value Questions for Market Maker Interviews
A market maker round does not test expected value the way a textbook does. This set is the overlap - the expected value questions that actually turn up in this format.
63 questions, all free to practise. The split is 6 easy, 24 medium, 33 hard.
- A coin that branches into a dieEasyCombinatoricsExpected ValueView →
- Expected flips for two heads (not in a row)EasyProbabilityExpected ValueView →
- Keep it or draw againEasyProbabilityExpected ValueView →
- Reflipping for valueEasyProbabilityExpected ValueView →
- Retries under a hard capEasyExpected ValueStochastic ProcessesView →
- Weighting a fixed sumEasyConditional Probability & ExpectationExpected ValueView →
- A convexity gap by JensenMediumRandom VariablesExpected ValueView →
- An ant returning to its cornerMediumExpected ValueStochastic ProcessesView →
- Boy–girl neighbors in a lineMediumCombinatoricsExpected ValueView →
- Expectation of e raised to a normalMediumRandom VariablesExpected ValueView →
- Expected ascents in a shuffleMediumCombinatoricsExpected ValueView →
- Expected duration of a fair gameMediumExpected ValueStochastic ProcessesView →
- Expected fives before the first sixMediumProbabilityExpected ValueView →
- Expected flips for HHMediumRandom VariablesExpected ValueView →
- Expected flips for HTMediumExpected ValueStochastic ProcessesView →
- Expected rolls for two sixes in a rowMediumExpected ValueStochastic ProcessesView →
- First to three of a kind in a rowMediumProbabilityExpected ValueView →
- Heads given the ends differMediumConditional Probability & ExpectationExpected ValueView →
- Inversions in a shuffleMediumCombinatoricsExpected ValueView →
- Is the random walk squared a martingale?MediumExpected ValueStochastic ProcessesView →
- Law of total varianceMediumConditional Probability & ExpectationExpected ValueView →
- Letters into envelopesMediumProbabilityExpected ValueView →
- Memoryless waitingMediumConditional Probability & ExpectationRandom VariablesView →
- Paid only if the last roll winsMediumExpected ValueView →
- Position of the first aceMediumConditional Probability & ExpectationExpected ValueView →
- Ratio of partial sumsMediumRandom VariablesExpected ValueView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- Rolls to a six before a fiveMediumProbabilityExpected ValueView →
- Rolls until a face repeatsMediumProbabilityExpected ValueView →
- k-th order statisticMediumExpected ValueStatisticsView →
- Bluffing frequency in pokerHardProbabilityExpected ValueView →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Connecting noodlesHardProbabilityExpected ValueView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Cycles in a shuffleHardCombinatoricsExpected ValueView →
- Dealing until kings or a king-and-aceHardCombinatoricsExpected ValueView →
- Deriving the first-price shading factorHardProbabilityExpected ValueView →
- Draws to beat a hidden uniformHardRandom VariablesExpected ValueView →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- Draws until a smaller valueHardExpected ValueView →
- Drunk man on a bridgeHardExpected ValueStochastic ProcessesView →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected chord between two random pointsHardProbabilityExpected ValueView →
- Expected flips for HHHHardExpected ValueStochastic ProcessesView →
- Expected flips for HTHHardExpected ValueStochastic ProcessesView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Expected local maxima in a shuffleHardProbabilityExpected ValueView →
- Four heads in a rowHardExpected ValueStochastic ProcessesView →
- Guessing cards from a known pileHardProbabilityExpected ValueView →
- Long cycles in a random permutationHardCombinatoricsExpected ValueView →
- Loops from tying noodlesHardProbabilityExpected ValueView →
- Optional stopping between +3 and −5HardExpected ValueStochastic ProcessesView →
- Overshoot past oneHardProbabilityRandom VariablesView →
- Pairs left in the drawerHardCombinatoricsExpected ValueView →
- Rolls to a six, given all evenHardConditional Probability & ExpectationExpected ValueView →
- Runs of red and blue marblesHardCombinatoricsExpected ValueView →
- Smallest card sharing a boxHardProbabilityExpected ValueView →
- The all-pay auctionHardProbabilityExpected ValueView →
- The decreasing run of uniformsHardRandom VariablesExpected ValueView →
- The two-envelopes paradoxHardProbabilityConditional Probability & ExpectationView →
- Uniforms summing past 1HardRandom VariablesExpected ValueView →
- World Series bettingHardExpected ValueStochastic ProcessesView →
Widen the search
This set is a slice of two larger ones. If it is too narrow, start here instead:
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