Probability Interview Questions for Traders
Traders get asked probability differently from other quant roles - the emphasis shifts with what the job actually does. This is that slice.
193 questions, 158 of them free to practise right now. The split is 91 easy, 76 medium, 26 hard.
- 1 immediately before 2EasyProbabilityCombinatoricsView →
- A dice sum divisible by threeEasyProbabilityView →
- A die decides how many balls to drawEasyProbabilityExpected ValueView →
- A die with one face decrementedEasyProbabilityConditional Probability & ExpectationView →
- A dry weekend, assuming independenceEasyProbabilityView →
- A heart or a king given redEasyProbabilityConditional Probability & ExpectationView →
- A perfect-power dice sumEasyProbabilityCombinatoricsView →
- A point is established in crapsEasyProbabilityView →
- A specific sequence given three headsEasyProbabilityConditional Probability & ExpectationView →
- A sum of four before a sum of twoEasyProbabilityView →
- A three given a sum divisible by threeEasyProbabilityConditional Probability & ExpectationView →
- Adjacent faces on two diceEasyProbabilityView →
- All four aces before any kingEasyProbabilityCombinatoricsView →
- All three land in the same halfEasyProbabilityRandom VariablesView →
- An even sum given a five appearsEasyProbabilityConditional Probability & ExpectationView →
- Ants on a squareEasyProbabilityBrainteasersView →
- At least one 3 and at least one 5EasyProbabilityView →
- At least one blue and one greenEasyProbabilityCombinatoricsView →
- At least one matching pair in three cardsEasyProbabilityCombinatoricsView →
- At least two in the windowEasyProbabilityStochastic ProcessesView →
- Backing out a parlay's hidden leg probabilityEasyProbabilityMarket Making & Betting GamesView →
- Beating a product of uniformsEasyProbabilityRandom VariablesView →
- Beating three othersEasyProbabilityRandom VariablesView →
- Both red among the top twoEasyProbabilityConditional Probability & ExpectationView →
- Conditioning a uniform waitEasyProbabilityRandom VariablesView →
- Counting arithmetic triplesEasyProbabilityCombinatoricsView →
- Counting flushesEasyProbabilityCombinatoricsView →
- Dots on distinct edgesEasyProbabilityCombinatoricsView →
- Drawing a matching pair of socksEasyProbabilityCombinatoricsView →
- Even count until the coin repeatsEasyProbabilityView →
- Even heads with one fair coinEasyProbabilityConditional Probability & ExpectationView →
- Even sum bigger than sevenEasyProbabilityView →
- Exactly one ace in three drawsEasyProbabilityCombinatoricsView →
- Exactly one head given at least oneEasyProbabilityConditional Probability & ExpectationView →
- 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 →
- Expected sets for a favored playerEasyProbabilityExpected ValueView →
- Expected sum given a sixEasyProbabilityExpected ValueView →
- Face card or heartEasyProbabilityView →
- Face or ace given a red cardEasyProbabilityConditional Probability & ExpectationView →
- Fair mid on a dice product that voids on doublesEasyProbabilityExpected ValueView →
- Fair price of a heads-majority betEasyProbabilityExpected ValueView →
- Finding the number of blue socksEasyProbabilityCombinatoricsView →
- First tail within two flipsEasyProbabilityView →
- Four dice summing to twentyEasyProbabilityCombinatoricsView →
- Hopping rabbitEasyProbabilityCombinatoricsView →
- How many rolls to make the 6-bet favorableEasyProbabilityMarket Making & Betting GamesView →
- Keep it or draw againEasyProbabilityExpected ValueView →
- Keep the d8 or gamble on the d12?EasyProbabilityExpected ValueView →
- Landing in the ringEasyProbabilityView →
- Matching a max and a min at zeroEasyProbabilityView →
- Matching head countsEasyProbabilityCombinatoricsView →
- Maximum of four uniforms in a bandEasyProbabilityRandom VariablesView →
- More heads than tails in six flipsEasyProbabilityView →
- One blue die matches the redEasyProbabilityView →
- Origin between two pointsEasyProbabilityView →
- Paid the last roll before you stopEasyProbabilityExpected ValueView →
- Probability two dice sum to a primeEasyProbabilityCombinatoricsView →
- Product divisible by fourEasyProbabilityView →
- Reflipping for valueEasyProbabilityExpected ValueView →
- Rolling until a high face, at a costEasyProbabilityExpected ValueView →
- Rolling until you match the first rollEasyProbabilityExpected ValueView →
- Rolls until an even sumEasyProbabilityExpected ValueView →
- Same side four timesEasyProbabilityView →
- Second roll beats the firstEasyProbabilityView →
- Stop at the first girlEasyProbabilityView →
- Streak then a head countEasyProbabilityConditional Probability & ExpectationView →
- The added babyEasyProbabilityConditional Probability & ExpectationView →
- The costliest roulette bet on the tableEasyProbabilityExpected ValueView →
- The higher die shows a fourEasyProbabilityView →
- The second draw is redEasyProbabilityConditional Probability & ExpectationView →
- The top two cards form a pairEasyProbabilityCombinatoricsView →
- Three cube faces at a cornerEasyProbabilityCombinatoricsView →
- Three dice, increasingEasyProbabilityCombinatoricsView →
- Three distinct dice, no sixEasyProbabilityCombinatoricsView →
- Three primes in six rollsEasyProbabilityView →
- Three-dice total given the firstEasyProbabilityConditional Probability & ExpectationView →
- Top three dice summing to eighteenEasyProbabilityCombinatoricsView →
- Two mismatched diceEasyProbabilityView →
- Two numbers in different groupsEasyProbabilityCombinatoricsView →
- Two primes with an even sumEasyProbabilityCombinatoricsView →
- Unchanged after ten swingsEasyProbabilityBrainteasersView →
- Ways to reach deuceEasyProbabilityCombinatoricsView →
- Whether either bus comes soonEasyProbabilityRandom VariablesView →
- Which side holds the heavy weightEasyProbabilityCombinatoricsView →
- Who wins the first head?EasyProbabilityView →
- Winning by a growing marginEasyProbabilityBrainteasersView →
- A 5 before a 7MediumProbabilityView →
- A low medianMediumProbabilityRandom VariablesView →
- 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 →
- 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 value of the highest cardMediumProbabilityExpected ValueView →
- 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 times as long to the first headMediumProbabilityRandom VariablesView →
- Full housesMediumProbabilityCombinatoricsView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- No face card before the two of heartsMediumProbabilityCombinatoricsView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- 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 →
- Sum versus twice the differenceMediumProbabilityRandom VariablesView →
- Tennis: two sets or three?MediumProbabilityView →
- The birthday problemMediumProbabilityCombinatoricsView →
- 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 →
- Two childrenMediumProbabilityConditional Probability & ExpectationView →
- Variance of the longer pieceMediumProbabilityRandom VariablesView →
- Which deck for two reds?MediumProbabilityView →
- A coin thick enough to land on its sideHardProbabilityBrainteasersView →
- A small sub-triangleHardProbabilityRandom VariablesView →
- A three-way race to the first headHardProbabilityRandom VariablesView →
- Expected chord between two random pointsHardProbabilityExpected ValueView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected local maxima in a shuffleHardProbabilityExpected ValueView →
- Guessing cards from a known pileHardProbabilityExpected ValueView →
- HTH before HHTHardProbabilityRandom VariablesView →
- Loops from tying noodlesHardProbabilityExpected ValueView →
- More coins, more heads?HardProbabilityCombinatoricsView →
- One of each face before the two of heartsHardProbabilityCombinatoricsView →
- Rolling until two rolls are closeHardProbabilityExpected ValueView →
- Rounds to see all faces with two diceHardProbabilityExpected ValueView →
- 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 reroll advantage in a die duelHardProbabilityMarket Making & Betting GamesView →
- Two random segments overlappingHardProbabilityRandom VariablesView →
- Will the three-legged table stand?HardProbabilityView →
- Both sixes given at least oneEasyProbabilityConditional Probability & Expectation Premium
- The first die beats the secondEasyProbabilityConditional Probability & Expectation Premium
- Absorption probability on a lineMediumProbabilityStochastic Processes Premium
- An ace in the handMediumProbabilityCombinatorics Premium
- At least two sixes in five rollsMediumProbabilityRandom Variables Premium
- Both even given an even sumMediumProbabilityConditional Probability & Expectation Premium
- Break-even half-spread from toxic flowMediumProbabilityExpected Value Premium
- Buyer count in a thinned arrival streamMediumProbabilityStochastic Processes Premium
- Counting straightsMediumProbabilityCombinatorics Premium
- Expected revenue of a Vickrey auctionMediumProbabilityExpected Value Premium
- First to roll a sixMediumProbability Premium
- Five distinct ranksMediumProbabilityCombinatorics Premium
- Four distinct birth monthsMediumProbabilityCombinatorics Premium
- HT before HH in coin flipsMediumProbabilityStochastic Processes Premium
- Large sum given a sixMediumProbabilityConditional Probability & Expectation Premium
- Minimum defense frequency against a betMediumProbabilityExpected Value Premium
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & Expectation Premium
- Neither die exceeds fourMediumProbabilityRandom Variables Premium
- Prime sumMediumProbability Premium
- Rare-event Poisson approximationMediumProbabilityRandom Variables Premium
- Second-price auction strategyMediumProbabilityMarket Making & Betting Games Premium
- Sum of 10 with three diceMediumProbabilityCombinatorics Premium
- The larger die shows a 4MediumProbabilityRandom Variables Premium
- Two face cardsMediumProbabilityCombinatorics Premium
- Two reds in a row from a shrinking urnMediumProbabilityConditional Probability & Expectation Premium
- Two uniforms summing below a halfMediumProbabilityRandom Variables Premium
- Two uniforms summing past 1.5MediumProbabilityCalculus Premium
- Which coin produced two heads?MediumProbabilityConditional Probability & Expectation Premium
- Winning from deuceMediumProbabilityConditional Probability & Expectation Premium
- Within distance d on the unit intervalMediumProbabilityCalculus Premium
- Best-of-seven underdogHardProbabilityRandom Variables Premium
- Bluffing frequency in pokerHardProbabilityExpected Value Premium
- Counting two-pair handsHardProbabilityCombinatorics Premium
- Deriving the first-price shading factorHardProbabilityExpected Value Premium
- The all-pay auctionHardProbabilityExpected Value Premium
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