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Interview prep / Probability

Probability interview questions: page 12 of 19

Questions 551–600

  1. Fives thrown before the first sixMedium
  2. Toasted pancake flipped overEasy
  3. Random point in the lower half of a coneEasy
  4. Normal point above a 60 degree line given positive YMedium
  5. Variance of the fourth power of a lognormalMedium
  6. Odd row and column sums in a random 3 by 3 gridMedium
  7. All-different win totals in a 32-team round robinEasy
  8. Cards between the first two and the first aceHard
  9. Biased coin maximising one run of exactly two headsMedium
  10. Expected number of same-colour blocks in 25 cellsMedium
  11. Rock paper scissors against a player who never throws rockEasy
  12. Expectation of X squared over Y for a product densityEasy
  13. Bus wait when some gaps include an hour-long refuelMedium
  14. Three random dots on different sides of a squareEasy
  15. Odd sums on every row, column and diagonal of a 3 by 3Medium
  16. Variance of hatched eggs from a Poisson laying countEasy
  17. Staff size maximising expected birthday holiday hoursMedium
  18. Random divisor of 20 factorial being a multiple of 20Medium
  19. Optimal stake in a token pool gameHard
  20. Obtuse triangle from three random points on a circleMedium
  21. Two-headed coin among a hundred after one headEasy
  22. Standard deviation of the sum of two cards labelled 0 to 4Easy
  23. Rotating train cars into red, green, blueEasy
  24. Two diners arriving within ten minutes of each otherMedium
  25. Turning up air and water before fireEasy
  26. Expected number of car platoons on a long roadHard
  27. Divisor of ten to the 99 that is a multiple of ten to the 80Easy
  28. Card following an ace that first appears at position 27Medium
  29. Second moment from a given mean and varianceEasy
  30. Mean of an average of squared and product termsEasy
  31. Three friends sharing a weekday of birthEasy
  32. A run of exactly four dogs at a round tableMedium
  33. Rejection sampling a Beta(3,2) with the tightest boxMedium
  34. Length giving one increasing run of six on averageEasy
  35. At least one of three darts in the bullseye discEasy
  36. Expected number of four-card subsets from a Poisson boxHard
  37. No heads in a Poisson number of fair tossesEasy
  38. Visits to 1000 before 0 for a walk started at 5Hard
  39. Three darts in three different ringsEasy
  40. Pure equilibria when one player wants distanceEasy
  41. Uniform plus exponential exceeding oneEasy
  42. Choosing which consecutive die pair to wait forMedium
  43. Free throws where success rate copies past accuracyMedium
  44. Variance of the heart count in an eight-card handEasy
  45. Ten-digit codes that fall then riseMedium
  46. Finishing a slice in the next minuteEasy
  47. Dice game paying the first non-seven totalMedium
  48. Expected value of seven bills from a box of eightEasy
  49. Lattice paths in 3D to the point (3,4,5)Easy
  50. Correlation of two sums sharing a common termEasy