id stringlengths 15 21 | topic stringclasses 5
values | difficulty stringclasses 3
values | question stringlengths 25 475 | answer float64 0 233k | worked_answer stringlengths 116 128 |
|---|---|---|---|---|---|
probability-001 | probability | easy | A fair coin is tossed three times. What is the probability of at least one head? | 0.875 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-001 |
probability-002 | probability | easy | Two fair dice are rolled. What is the probability the sum is 7? | 0.166667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-002 |
probability-003 | probability | easy | You roll a pair of fair dice. How likely is a total of 10 or more? | 0.166667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-003 |
probability-004 | probability | easy | What is the expected value of one roll of a fair six-sided die? | 3.5 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-004 |
probability-005 | probability | easy | How many rolls of a fair die do you expect to need to see the first six? | 6 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-005 |
probability-006 | probability | medium | How many rolls of a fair die do you expect to need to see two sixes in a row? | 42 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-006 |
probability-007 | probability | medium | How many tosses of a fair coin do you expect before you first see two heads in a row (HH)? | 6 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-007 |
probability-008 | probability | medium | How many tosses of a fair coin do you expect before you first see a head followed immediately by a tail (HT)? | 4 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-008 |
probability-009 | probability | medium | A family has two children, and at least one of them is a boy. What is the probability both are boys? | 0.333333 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-009 |
probability-010 | probability | easy | A family has two children and the older one is a boy. What is the probability both are boys? | 0.5 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-010 |
probability-011 | probability | easy | In the Monty Hall game you pick a door; the host, who knows where the car is, opens another door showing a goat and offers a switch. What is your probability of winning if you switch? | 0.666667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-011 |
probability-013 | probability | medium | A stick of length 1 is broken at two points chosen independently and uniformly. What is the probability the three pieces form a triangle? | 0.25 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-013 |
probability-018 | probability | medium | Three points are placed independently and uniformly on a circle. What is the probability they all lie in some semicircle? | 0.75 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-018 |
probability-019 | probability | hard | Four points are placed independently and uniformly on a circle. What is the probability they all lie in some semicircle? | 0.5 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-019 |
probability-020 | probability | medium | How many rolls of a fair die do you expect to need until every face has appeared at least once? | 14.7 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-020 |
probability-021 | probability | medium | You start with £3 and bet £1 on each toss of a fair coin until you reach £10 or go broke. What is the probability you reach £10? | 0.3 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-021 |
probability-022 | probability | hard | In the same game (start £3, stop at £0 or £10, fair coin), what is the expected number of tosses? | 21 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-022 |
probability-024 | probability | easy | Two cards are drawn from a standard deck without replacement. What is the probability both are aces? | 0.004525 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-024 |
probability-025 | probability | medium | What is the probability a five-card poker hand is a flush (including straight flushes)? | 0.001981 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-025 |
probability-026 | probability | medium | What is the probability of at least one six in four rolls of a fair die? | 0.517747 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-026 |
probability-027 | probability | medium | What is the probability of at least one double six in 24 rolls of two dice? | 0.491404 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-027 |
probability-028 | probability | medium | A disease affects 1% of a population. A test detects it 99% of the time and gives a false positive 5% of the time. Given a positive test, what is the probability of having the disease? | 0.166667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-028 |
probability-029 | probability | easy | An urn holds 3 red and 2 blue balls. Two are drawn without replacement. What is the probability they are the same colour? | 0.4 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-029 |
probability-030 | probability | medium | Ten letters are placed at random into their ten addressed envelopes. What is the expected number in the correct envelope? | 1 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-030 |
probability-031 | probability | hard | A 52-card deck is shuffled. Approximately what is the probability that no card is in its original position? | 0.367879 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-031 |
probability-032 | probability | medium | A fair die is rolled six times. What is the expected number of distinct faces seen? | 3.990612 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-032 |
probability-034 | probability | medium | You roll a die and may roll once more, keeping only the second result. With optimal play, what is your expected payout (face value)? | 4.25 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-034 |
probability-035 | probability | hard | As before, but you may roll up to three times in total, keeping the last roll. What is the optimal expected payout? | 4.666667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-035 |
probability-036 | probability | easy | You are paid the square of a fair die roll. What is the expected payout? | 15.166667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-036 |
probability-037 | probability | medium | Two fair dice are rolled. What is the expected value of the larger? | 4.472222 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-037 |
probability-038 | probability | easy | Two fair dice are rolled. What is the expected value of their product? | 12.25 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-038 |
probability-039 | probability | medium | Two fair dice are rolled. What is the expected absolute difference? | 1.944444 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-039 |
probability-040 | probability | hard | A needle of length 1 is dropped at random on a floor ruled with parallel lines 1 apart. What is the probability it crosses a line? | 0.63662 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-040 |
probability-042 | probability | medium | A coin is tossed until either HHH or THH appears. What is the probability HHH comes first? | 0.125 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-042 |
probability-043 | probability | medium | How many tosses of a fair coin do you expect before you first see three heads in a row? | 14 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-043 |
probability-044 | probability | easy | Customers arrive as a Poisson process at 2 per hour. What is the probability of no arrivals in a given hour? | 0.135335 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-044 |
probability-045 | probability | easy | A bulb's lifetime is exponential with mean 1000 hours. It has already lasted 500 hours. What is its expected remaining lifetime? | 1,000 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-045 |
probability-049 | probability | hard | A stick is broken at a uniform point, then the longer piece is broken at a uniform point. What is the probability the three pieces form a triangle? | 0.386294 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-049 |
probability-050 | probability | medium | A fair coin is tossed 10 times. What is the expected number of runs (maximal blocks of identical outcomes)? | 5.5 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-050 |
probability-051 | probability | easy | A simple symmetric random walk starts at 0. What is the probability it is back at 0 after exactly 2 steps? | 0.5 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-051 |
probability-052 | probability | easy | Two cards are drawn from a deck without replacement. What is the probability they are of different suits? | 0.764706 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-052 |
probability-053 | probability | easy | A fair coin is flipped until the first head appears. What is the expected number of flips? | 2 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-053 |
probability-054 | probability | medium | Three fair dice are rolled. What is the probability that all three show different numbers? | 0.555556 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-054 |
probability-055 | probability | medium | Two cards are drawn from a standard deck without replacement. What is the probability that both are hearts? | 0.058824 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-055 |
probability-057 | probability | medium | A stick of length 1 is broken at a uniformly random point. What is the expected length of the longer piece? | 0.75 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-057 |
probability-058 | probability | medium | Four people each take a hat at random from four hats. What is the probability that nobody takes their own? | 0.375 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-058 |
probability-059 | probability | medium | Two players take turns rolling a fair die, and the first to roll a six wins. What is the probability that the player who rolls first wins? | 0.545455 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-059 |
probability-060 | probability | medium | Ten balls are thrown independently into ten boxes, each ball landing in any box with equal probability. What is the expected number of empty boxes? | 3.486784 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-060 |
probability-061 | probability | hard | Ten distinct numbers arrive one at a time in random order. A number is a *record* if it exceeds everything before it. What is the expected number of records? | 2.928968 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-061 |
probability-063 | probability | hard | How many tosses of a fair coin are expected before the pattern HTH first appears? | 10 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-063 |
probability-064 | probability | hard | How many tosses of a fair coin are expected before the pattern HHT first appears? | 8 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-064 |
probability-065 | probability | hard | Your opponent chooses the pattern HHT. You then choose your own three-toss pattern, and whichever appears first in a sequence of fair tosses wins. What is your winning probability under the best choice? | 0.75 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-065 |
probability-067 | probability | hard | Ten people leave identical hats at a cloakroom and receive them back at random. What is the probability nobody gets his own hat? | 0.367879 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-067 |
probability-069 | probability | hard | 100 prisoners are numbered 1 to 100. In a room are 100 closed boxes, each holding one of the numbers in random order. Each prisoner enters alone, may open 50 boxes, and must find his own number; all must succeed or all are executed. They may agree a strategy beforehand but cannot communicate once it starts. What is the... | 0.311828 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-069 |
probability-070 | probability | hard | A stick of length 1 is broken at two independent uniform points. What is the expected length of the shortest of the three pieces? | 0.111111 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-070 |
probability-071 | probability | medium | Three points are chosen independently and uniformly on a circle. What is the probability the triangle they form is acute? | 0.25 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-071 |
probability-072 | probability | medium | Three cards sit in a hat: one red on both sides, one white on both sides, one red on one side and white on the other. You draw one and see red. What is the probability the other side is red? | 0.666667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-072 |
probability-073 | probability | hard | A man has two children. At least one is a boy born on a Tuesday. What is the probability both are boys? | 0.481481 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-073 |
probability-074 | probability | hard | A fair die is rolled 10 times. What is the expected number of distinct faces seen? | 5.030995 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-074 |
probability-075 | probability | medium | Buses arrive as a Poisson process, on average one every 10 minutes. You arrive at the stop at a random moment. How long do you expect to wait? | 10 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-075 |
probability-079 | probability | hard | A random chord of a circle is drawn by picking its two endpoints independently and uniformly on the circumference. What is the probability it is longer than the side of the inscribed equilateral triangle? | 0.333333 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-079 |
probability-080 | probability | hard | In the casino game of craps you roll two dice. You win at once on 7 or 11 and lose at once on 2, 3 or 12. Any other total becomes your *point*, and you then roll until either the point repeats (win) or a 7 appears (lose). What is your probability of winning? | 0.492929 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-080 |
probability-081 | probability | medium | Two fair dice are rolled repeatedly. What is the probability a total of 8 appears before a total of 7? | 0.454545 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-081 |
probability-082 | probability | hard | An ant starts at one corner of a cube and each minute walks along a randomly chosen edge to an adjacent corner. How many minutes are expected before it first reaches the opposite corner? | 10 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-082 |
probability-083 | probability | medium | A fair coin is tossed 10 times. Given that at least one head appeared, what is the probability all ten were heads? | 0.000978 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-083 |
probability-084 | probability | hard | You are dealt 13 cards from a well-shuffled standard deck. What is the expected number of distinct suits in your hand? | 3.948836 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-084 |
probability-085 | probability | hard | Two people agree to meet between noon and one o'clock, each arriving at a uniformly random time and waiting exactly 15 minutes before leaving. What is the probability they meet? | 0.4375 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-085 |
probability-088 | probability | medium | In a room of 30 people, what is the expected number of pairs sharing a birthday? (Ignore leap years.) | 1.191781 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-088 |
probability-089 | probability | easy | Three cards are drawn from a standard deck without replacement. What is the probability that all three are red? | 0.117647 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-089 |
probability-090 | probability | easy | A fair die is rolled twice. What is the probability that the second roll is strictly greater than the first? | 0.416667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-090 |
probability-091 | probability | easy | A fair coin is tossed until both a head and a tail have appeared. What is the expected number of tosses? | 3 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-091 |
probability-092 | probability | medium | A fair coin is tossed four times. What is the probability that no two consecutive tosses are both heads? | 0.5 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-092 |
probability-097 | probability | hard | A fair die is rolled until a six appears. Given that every roll in the sequence showed an even number, what is the expected number of rolls? | 1.5 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-097 |
probability-098 | probability | easy | Three friends each toss a fair coin; if exactly one shows a different face from the other two, that person pays. If all three match, they toss again. What is the expected number of rounds? | 1.333333 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-098 |
probability-099 | probability | medium | A bag holds two coins: one fair, one with heads on both sides. You pick one at random and toss it three times, getting three heads. What is the probability you picked the double-headed coin? | 0.888889 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-099 |
probability-100 | probability | medium | A fair coin is tossed five times. What is the probability of a run of at least three consecutive heads? | 0.25 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-100 |
probability-101 | probability | medium | A point is chosen uniformly at random in a unit square. What is its expected distance to the nearest side? | 0.166667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-101 |
probability-102 | probability | medium | What is the probability that a five-card poker hand contains exactly one pair and nothing better? | 0.422569 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-102 |
probability-107 | probability | medium | Two fair dice are rolled and you are told at least one shows a six. What is the probability that both show a six? | 0.090909 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-107 |
probability-109 | probability | hard | 100 passengers board a full plane one at a time. The first has lost their boarding pass and takes a seat uniformly at random. Each later passenger takes their own seat if it is free, and otherwise a free seat at random. What is the probability the last passenger gets their own seat? | 0.5 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-109 |
probability-110 | probability | hard | A stick of length 1 is cut at three points chosen independently and uniformly. What is the probability the four pieces can form a quadrilateral? | 0.5 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-110 |
probability-111 | probability | hard | In an election, candidate A receives 6 votes and B receives 4. The ballots are counted one at a time in random order. What is the probability A is strictly ahead throughout the count? | 0.2 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-111 |
probability-113 | probability | medium | A point is chosen uniformly at random inside a disc of radius 1. What is its expected distance from the centre? | 0.666667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-113 |
probability-114 | probability | hard | Two points are chosen independently and uniformly on a circle of radius 1. What is the expected length of the chord joining them? | 1.27324 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-114 |
probability-116 | probability | hard | A fair die is rolled until a six appears. What is the expected sum of all the rolls before the six? | 15 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-116 |
probability-117 | probability | medium | A fair die is rolled until two consecutive rolls show the same number. What is the expected total number of rolls? | 7 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-117 |
probability-119 | probability | hard | Ten people stand in a room. At a signal, each fires a water pistol at one of the other nine, chosen uniformly and independently. What is the expected number of people left dry? | 3.464394 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-119 |
probability-121 | probability | hard | A simple symmetric random walk starts at 0 and takes 10 steps. What is the expected number of times it returns to 0 (not counting the start)? | 1.707031 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-121 |
probability-122 | probability | medium | Three fair dice are rolled in order. What is the probability the three numbers are strictly increasing? | 0.092593 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-122 |
probability-123 | probability | medium | Three fair dice are rolled. What is the expected value of the smallest of the three numbers? | 2.041667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-123 |
probability-124 | probability | easy | An integer is chosen at random from 1 to 100. What is the probability that it shares no common factor greater than 1 with 100? | 0.4 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-124 |
probability-126 | probability | hard | A fair die is rolled until the running total is at least 7. What is the expected number of rolls? Give your answer to two decimal places. | 2.521626 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-126 |
probability-127 | probability | hard | A fair die is rolled until the running total is at least 100. Approximately how many rolls does this take on average? Give your answer to one decimal place. | 29.0476 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-127 |
probability-128 | probability | medium | What is the probability that a five-card poker hand is a full house? | 0.001441 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-128 |
probability-129 | probability | easy | Two fair dice are rolled and their sum is 8. What is the expected value of the first die? | 4 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-129 |
probability-130 | probability | medium | Ten fair dice are rolled. What is the variance of their total? | 29.166667 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-130 |
probability-131 | probability | medium | Two fair dice are rolled. What is the probability that the product of the two numbers is a perfect square? | 0.222222 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-131 |
probability-135 | probability | medium | A fair die is rolled four times. What is the probability that the largest number rolled is exactly 5? | 0.284722 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-135 |
probability-137 | probability | medium | A fair die is rolled until both a 1 and a 6 have appeared. What is the expected number of rolls? | 9 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-137 |
probability-138 | probability | medium | A standard 52-card deck is shuffled and dealt face up, one card at a time. What is the expected position of the first ace? | 10.6 | https://geodesicpartners.co.uk/quant-questions-probability?utm_source=huggingface&utm_medium=dataset#probability-138 |
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Quant interview questions with numeric answers
Here you'll find 241 questions like the ones candidates meet when they apply for quant trading and research roles. Most are probability puzzles and brainteasers, though a few on expected value and market making are mixed in. Whatever the question, the reply it calls for is a single figure.
Because of that, the set may turn out more useful than you'd expect. Nobody has to write out an explanation, so you can treat the collection as a small mathematics benchmark and mark a model automatically with a tolerance check.
A row holds an id and a topic, a difficulty label (easy, medium or hard), the question in plain text and the answer as a numeric value. Fractions are written as decimals to ten places. With that in mind, I'd mark with a tolerance of about 1e-6. Worked solutions sit behind the link in the worked_answer field.
Code computed and checked the answers when they first went into our question bank. While preparing this upload I also reworked a handful by hand, and the one-pair poker hand is a good example: it comes to 1,098,240 hands out of 2,598,960, or about 0.4226.
If you're getting ready for quant interviews yourself, you'll probably find the questions easier to learn from on the site, where they're timed and all the solutions are written out in detail: https://geodesicpartners.co.uk/quant-questions-probability
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