Quant interview questions

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• Two fair dice are rolled and you are told at least one shows a six.Probability · Applied
• How many people are needed before the probability that two share a birthday…Probability · Applied
• Orders arrive as a Poisson process averaging four per minute.Probability · Applied
• For a positive random variable X that is not constant, how do 𝔼[1/X] and 1/𝔼[X] compare?Probability · Applied
• Cereal boxes each contain one of ten equally likely coupons.Probability · Applied
• How many flips of a fair coin are needed, on average, to see three heads in a row?Probability · Applied
• A fair six-sided die is rolled six times.Probability · Applied
• You roll a fair die and then flip that many fair coins.Probability · Applied
• A symmetric random walk starts at 0 and stops the first time it reaches +3 or −2.Probability · Applied
• Thirty people are in a room and birthdays are uniform over 365 days.Probability · Applied
• A prize is behind one of 100 doors.Probability · Applied
• You may re-roll a fair six-sided die as often as you like, paying $1 each time you do.Probability · Advanced
• You may re-roll a fair hundred-sided die as often as you like, paying $1 each time.Probability · Advanced
• Derive the value of the game in which you may re-roll a fair n-sided die as…Probability · Advanced
• A family has two children.Probability · Advanced
• Flipping a fair coin, which takes longer on average: the first occurrence of…Probability · Advanced
• A coin lands heads with probability 0.6.Probability · Advanced
• How many fair coin flips are needed on average to first see the pattern HTH?Probability · Advanced
• A symmetric random walk starts at the origin.Probability · Advanced
• A stick of length one is broken at two points chosen independently and uniformly along it.Probability · Advanced
• Three points are chosen independently and uniformly on a circle.Probability · Advanced
• X and Y are independent standard normals.Probability · Advanced
• The same walk – symmetric, starting at 0, stopped at +3 or −2.Probability · Advanced
• For the single optional re-roll of a fair six-sided die, at what re-roll fee…Probability · Expert
• Assets A and B correlate at 0.8, and B and C also at 0.8.Probability · Expert
• You choose the pattern HHH and your opponent, choosing afterwards, picks THH.Probability · Expert
• You draw independent uniforms on [0,1] until their running sum exceeds one.Probability · Expert
• The pot holds $60 and your opponent bets $30.Games, decision theory and puzzles · Foundation
• You roll a fair die and may re-roll once, keeping the second value if you do.Games, decision theory and puzzles · Applied · Free solution
• In the secretary problem, what is the probability the optimal policy finds the…Games, decision theory and puzzles · Applied
• Twelve coins, one counterfeit and either heavier or lighter.Games, decision theory and puzzles · Applied
• In a zero-sum game, what characterises your opponent’s optimal mixing frequencies?Games, decision theory and puzzles · Applied
• You have two eggs and a 100-storey building.Games, decision theory and puzzles · Applied
• Nim with piles of 3, 4 and 5: you move first and the player taking the last counter wins.Games, decision theory and puzzles · Applied
• In a sealed-bid auction where the winner pays the second-highest bid, what should you bid?Games, decision theory and puzzles · Applied
• Everyone names a number in [0,100] and whoever is closest to two thirds of the…Games, decision theory and puzzles · Applied
• Twenty-five horses, a track that races five at a time, and no timing device.Games, decision theory and puzzles · Applied
• You may roll a fair die up to three times and are paid the face value of the…Games, decision theory and puzzles · Applied
• A fair coin is flipped until the first tail.Games, decision theory and puzzles · Applied
• A six-chamber revolver holds two bullets in adjacent chambers.Games, decision theory and puzzles · Applied