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Interview prep / Probability

Probability interview questions: page 3 of 19

Questions 101–150

  1. Exponential bulb outliving ten bulbs used in sequenceMedium
  2. Mean squared distance of a ten-step random walkMedium
  3. Packing small cubes into a cube of side twentyEasy
  4. Right triangle with uniform legs: angle above 45 degreesEasy
  5. Archer with a 75 percent hit rate over three shotsEasy
  6. Expected overshoot sum when uniforms first pass oneHard
  7. Making a biased-coin race against a fair coin evenEasy
  8. Rolls needed to see every face of a dieEasy
  9. Betting 20 dollars on a number across three diceEasy
  10. Removing the X component to decorrelate YEasy
  11. Draws with replacement until every suit appearsMedium
  12. Generating function of a geometric variable at one thirdEasy
  13. Mean absolute gap between two independent normalsMedium
  14. Die with the first rolled face removedMedium
  15. Standard deviation of a negatively correlated sumEasy
  16. Paying 5 cents per extra uniform draw, chosen upfrontMedium
  17. One paid reroll of a die costing a dollarEasy
  18. Chance a five-card hand is exactly two pairEasy
  19. Frog on a ring of 100 pads reaching the far pad lastMedium
  20. Coin flips needed to simulate a one-third eventEasy
  21. Expected smallest roll seen before the first fiveMedium
  22. Waiting time for two consecutive headsEasy
  23. Expected letters reaching the right firm at randomEasy
  24. Extinction chance for a colony that starts with three cellsEasy
  25. Accident in half an hour given the hourly chanceEasy
  26. Success probability that makes eight of twelve most likelyEasy
  27. Prize door found with a wheel that sometimes tellsEasy
  28. Restoring a six-digit house number after two digits fallEasy
  29. Higher or lower on a d100 paid the second valueMedium
  30. Two random triangles on six points sharing a cornerEasy
  31. Swimmer 2 second and swimmer 5 among the medalsEasy
  32. Random bit flips on the 2x2 identity until singularMedium
  33. Unlimited dollar rerolls of a dieMedium
  34. Uniform gap above a half given the sum is below oneEasy
  35. Mother of two at a conference for parents of girlsEasy
  36. Second dart forced farther out than the firstHard
  37. Twelve food units shared among four of ten kidsMedium
  38. Keep rolling while you repeat the first die valueMedium
  39. Distinct sums of three products from shuffling 1 to 6Medium
  40. Two uniform points on an interval straddling zeroEasy
  41. Frog tour of eight pads with a single backward hopHard
  42. Three dice whose range is exactly fourMedium
  43. Switching doors after the host reveals a goatMedium
  44. Average of the lowest of three diceHard
  45. Limiting chance a random map has five fixed pointsEasy
  46. Exactly three primes in six die rollsEasy
  47. Three random legs on a round table all 90 degrees apartHard
  48. Seven people around a table sorted by ageEasy
  49. Both blue and green appear in four draws with replacementEasy
  50. Expected smallest gap among 101 uniform pointsHard