| const C=[{"q": "A fair die is rolled twice. What is the probability that the second roll is strictly greater than the first?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-090"}, {"q": "What is the product of all the positive divisors of 12?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-104"}, {"q": "You roll a fair die and are paid its face value in pounds. You may pay £1 to roll once more, in which case you must accept the second roll. Playing optimally, what is the game worth?", "u": "https://geodesicpartners.co.uk/quant-questions-market-making?utm_source=social&utm_medium=post#market-making-039"}, {"q": "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?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-011"}, {"q": "Customers arrive as a Poisson process at 2 per hour. What is the probability of no arrivals in a given hour?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-044"}, {"q": "A classifier has 40 true positives and 10 false positives. What is its precision?", "u": "https://geodesicpartners.co.uk/quant-questions-statistics-ml?utm_source=social&utm_medium=post#statistics-ml-008"}, {"q": "A stick of length 1 is broken at a uniformly random point. What is the expected length of the longer piece?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-057"}, {"q": "What is the smallest number of moves a knight needs to go from one corner of a chessboard (a1) to the opposite corner (h8)?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-086"}, {"q": "A fair coin is tossed 10 times. What is the expected number of runs (maximal blocks of identical outcomes)?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-050"}, {"q": "How many five-digit numbers are divisible by 3 and contain at least one digit 6?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-113"}, {"q": "What is the largest number of knights that can be placed on a chessboard so that no two attack each other?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-094"}, {"q": "Four people each take a hat at random from four hats. What is the probability that nobody takes their own?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-058"}, {"q": "How many tosses of a fair coin are expected before the pattern HTH first appears?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-063"}, {"q": "In how many ways can you make £1 using only 50p, 20p and 10p coins?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-088"}, {"q": "Ten fair dice are rolled. What is the variance of their total?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-130"}, {"q": "A brick weighs 1 kg plus half a brick. How much does the brick weigh?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-080"}, {"q": "What is the angle between the hands of a clock at 9:30, in degrees?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-039"}, {"q": "Two uncorrelated assets each have 20% volatility. What is the volatility of an equal-weight portfolio, in %?", "u": "https://geodesicpartners.co.uk/quant-questions-statistics-ml?utm_source=social&utm_medium=post#statistics-ml-031"}, {"q": "How many strings of ten binary digits contain no two adjacent 1s?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-107"}, {"q": "How many rolls of a fair die do you expect to need to see two sixes in a row?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-006"}, {"q": "Three fair dice are rolled. What is the expected value of the smallest of the three numbers?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-123"}, {"q": "A stick of length 1 is broken at two points chosen independently and uniformly. What is the probability the three pieces form a triangle?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-013"}, {"q": "What is the probability a five-card poker hand is a flush (including straight flushes)?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-025"}, {"q": "A book's daily P&L is normally distributed with mean 0 and standard deviation £10,000. What is its one-day 99% value at risk, to the nearest £100?", "u": "https://geodesicpartners.co.uk/quant-questions-market-making?utm_source=social&utm_medium=post#market-making-040"}, {"q": "10 people each shake hands once with every other person. How many handshakes?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-008"}, {"q": "Three points are chosen independently and uniformly on a circle. What is the probability the triangle they form is acute?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-071"}, {"q": "A queen stands in a corner of an empty chessboard. How many squares does she attack?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-095"}, {"q": "What is the largest prime factor of 1,001?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-105"}, {"q": "How many positive integers less than 1000 have only odd digits?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-073"}, {"q": "In how many ways can you climb 10 stairs taking 1 or 2 steps at a time?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-031"}, {"q": "In a room of 30 people, what is the expected number of pairs sharing a birthday? (Ignore leap years.)", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-088"}, {"q": "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.", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-126"}, {"q": "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?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-059"}, {"q": "There are 10 stacks of 10 coins. Every coin weighs 10 g except those in one stack, which weigh 11 g each. With a digital scale that reads exact weight, what is the minimum number of weighings needed to identify the heavy stack?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-049"}, {"q": "You test 20 strategies that truly have no edge, each at the 5% significance level. How many false positives do you expect?", "u": "https://geodesicpartners.co.uk/quant-questions-statistics-ml?utm_source=social&utm_medium=post#statistics-ml-032"}, {"q": "How many tosses of a fair coin do you expect before you first see three heads in a row?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-043"}, {"q": "Make a market on the product of two dice. What is the fair value?", "u": "https://geodesicpartners.co.uk/quant-questions-market-making?utm_source=social&utm_medium=post#market-making-002"}, {"q": "With two identical eggs and a 100-storey building, what is the minimum number of drops that guarantees finding the highest safe floor?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-006"}, {"q": "A population has standard deviation 10. What is the standard error of the mean of 100 observations?", "u": "https://geodesicpartners.co.uk/quant-questions-statistics-ml?utm_source=social&utm_medium=post#statistics-ml-014"}, {"q": "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?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-097"}, {"q": "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?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-065"}, {"q": "A fair coin is tossed four times. What is the probability that no two consecutive tosses are both heads?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-092"}, {"q": "A classifier has 40 true positives and 60 false negatives. What is its recall?", "u": "https://geodesicpartners.co.uk/quant-questions-statistics-ml?utm_source=social&utm_medium=post#statistics-ml-009"}, {"q": "Two fair dice are rolled. What is the expected absolute difference?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-039"}, {"q": "A stock is at 100 and in one year will be either 130 or 90. Interest rates are zero, and analysts give the up move a probability of 0.8. What is a one-year call struck at 100 worth?", "u": "https://geodesicpartners.co.uk/quant-questions-market-making?utm_source=social&utm_medium=post#market-making-036"}, {"q": "Make a market on the sum of the two highest of three fair dice. What is the fair value?", "u": "https://geodesicpartners.co.uk/quant-questions-market-making?utm_source=social&utm_medium=post#market-making-035"}, {"q": "A coin is tossed until either HHH or THH appears. What is the probability HHH comes first?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-042"}, {"q": "One coin is rolled without slipping all the way around the rim of a second, identical, fixed coin until it returns to its starting point. How many complete rotations does the moving coin make about its own centre?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-053"}, {"q": "In one full day of 24 hours, how many times are the hour and minute hands of a clock exactly at right angles?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-072"}, {"q": "A solid 3 by 3 by 3 cube is to be cut into 27 unit cubes. Cuts are straight planes, and after each cut the pieces may be rearranged freely. What is the minimum number of cuts?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-059"}, {"q": "Two opposite corners are cut from an 8 by 8 chessboard, leaving 62 squares. How many dominoes, each covering two adjacent squares, can be placed without overlap or overhang?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-047"}, {"q": "Using only 3p and 5p coins, what is the largest amount, in pence, that cannot be paid exactly?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-040"}, {"q": "25 horses, a track that races 5 at a time, no stopwatch. What is the minimum number of races needed to find the three fastest?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-005"}, {"q": "How many 1s are in the binary representation of 255?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-025"}, {"q": "How many tosses of a fair coin do you expect before you first see two heads in a row (HH)?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-007"}, {"q": "A bulb's lifetime is exponential with mean 1000 hours. It has already lasted 500 hours. What is its expected remaining lifetime?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-045"}, {"q": "A point is chosen uniformly at random in a unit square. What is its expected distance to the nearest side?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-101"}, {"q": "An urn holds 3 red and 2 blue balls. Two are drawn without replacement. What is the probability they are the same colour?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-029"}, {"q": "Every 4-digit number that uses each of the digits 1, 2, 3 and 4 exactly once is written down. What is the sum of all of them?", "u": "https://geodesicpartners.co.uk/quant-questions-brainteasers?utm_source=social&utm_medium=post#brainteasers-097"}, {"q": "Two fair dice are rolled and their sum is 8. What is the expected value of the first die?", "u": "https://geodesicpartners.co.uk/quant-questions-probability?utm_source=social&utm_medium=post#probability-129"}]; |
