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.
194 questions, all free to practise. The split is 91 easy, 77 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 →
- Both sixes given at least oneEasyProbabilityConditional 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 (not in a row)EasyProbabilityExpected 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 rabbit, up to three stepsEasyProbabilityCombinatoricsView →
- 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 →
- 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 →
- Seven before six or eightEasyProbabilityCombinatoricsView →
- 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 first die beats the secondEasyProbabilityConditional Probability & ExpectationView →
- 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 →
- Absorption probability on a lineMediumProbabilityStochastic ProcessesView →
- An ace for everyoneMediumProbabilityCombinatoricsView →
- An ace in every pileMediumProbabilityCombinatoricsView →
- An ace in the handMediumProbabilityCombinatoricsView →
- At least two sixes in five rollsMediumProbabilityRandom VariablesView →
- Bertrand's boxMediumProbabilityConditional Probability & ExpectationView →
- Both even given an even sumMediumProbabilityConditional Probability & ExpectationView →
- Break-even half-spread from toxic flowMediumProbabilityExpected ValueView →
- Buyer count in a thinned arrival streamMediumProbabilityStochastic ProcessesView →
- Cash out or bustMediumProbabilityExpected ValueView →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Coin sets the number of dice rollsMediumProbabilityConditional Probability & ExpectationView →
- Counting straightsMediumProbabilityCombinatoricsView →
- 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 revenue of a Vickrey auctionMediumProbabilityExpected 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 roll a sixMediumProbabilityView →
- First to three of a kind in a rowMediumProbabilityExpected ValueView →
- Five distinct ranksMediumProbabilityCombinatoricsView →
- Four distinct birth monthsMediumProbabilityCombinatoricsView →
- 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 →
- HT before HH in coin flipsMediumProbabilityStochastic ProcessesView →
- Large sum given a sixMediumProbabilityConditional Probability & ExpectationView →
- Minimum defense frequency against a betMediumProbabilityExpected ValueView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- Monty Hall with 100 doorsMediumProbabilityConditional Probability & ExpectationView →
- Neither die exceeds fourMediumProbabilityRandom VariablesView →
- No face card before the two of heartsMediumProbabilityCombinatoricsView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- Painted cube, one face showingMediumProbabilityBrainteasersView →
- Prime sumMediumProbabilityView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Product of two uniforms above a halfMediumProbabilityRandom VariablesView →
- Rare-event Poisson approximationMediumProbabilityRandom 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 →
- Second-price auction strategyMediumProbabilityMarket Making & Betting GamesView →
- Sum of 10 with three diceMediumProbabilityCombinatoricsView →
- Sum versus twice the differenceMediumProbabilityRandom VariablesView →
- Tennis: two sets or three?MediumProbabilityView →
- The birthday problemMediumProbabilityCombinatoricsView →
- The larger die shows a 4 - what about the smaller?MediumProbabilityRandom VariablesView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- The third shiny pennyMediumProbabilityCombinatoricsView →
- The two-headed coinMediumProbabilityConditional Probability & ExpectationView →
- Three dots, exactly one shared edgeMediumProbabilityCombinatoricsView →
- Three ones in a rowMediumProbabilityCombinatoricsView →
- Three prisonersMediumProbabilityConditional Probability & ExpectationView →
- Two childrenMediumProbabilityConditional Probability & ExpectationView →
- Two face cardsMediumProbabilityCombinatoricsView →
- Two reds in a row from a shrinking urnMediumProbabilityConditional Probability & ExpectationView →
- Two uniforms summing below a halfMediumProbabilityRandom VariablesView →
- Two uniforms summing past 1.5MediumProbabilityCalculusView →
- Variance of the longer pieceMediumProbabilityRandom VariablesView →
- Which coin produced two heads?MediumProbabilityConditional Probability & ExpectationView →
- Which deck for two reds?MediumProbabilityView →
- Winning from deuceMediumProbabilityConditional Probability & ExpectationView →
- Within distance d on the unit intervalMediumProbabilityCalculusView →
- A coin thick enough to land on its sideHardProbabilityBrainteasersView →
- A small sub-triangleHardProbabilityRandom VariablesView →
- A three-way race to the first headHardProbabilityRandom VariablesView →
- Best-of-seven underdogHardProbabilityRandom VariablesView →
- Bluffing frequency in pokerHardProbabilityExpected ValueView →
- Counting two-pair handsHardProbabilityCombinatoricsView →
- Deriving the first-price shading factorHardProbabilityExpected ValueView →
- 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 all-pay auctionHardProbabilityExpected 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 →
Widen the search
This set is a slice of two larger ones. If it is too narrow, start here instead:
Practise these free
Create a free account to check your answers, track what you have solved, and run the timed simulators.