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Interview prep / Probability

Probability interview questions: page 6 of 19

Questions 251–300

  1. Two parked cars creeping forward to spaces 3 and 4Hard
  2. Expected tosses until HHHMedium
  3. Students majoring in neither English nor HistoryEasy
  4. Two walkers returning home with one always behindHard
  5. Bouncing particles leaving a one-metre rodHard
  6. Exactly two fives before seeing both 4 and 6Hard
  7. Cash needed to buy two normally priced jerseysEasy
  8. Maximum of four Unif(0,4) draws in (2,3]Easy
  9. Expected determinant of A minus its transposeEasy
  10. Ways to nest some of seven distinct dollsEasy
  11. Free throws where accuracy follows past successMedium
  12. Urn where black balls get swapped for redEasy
  13. Matching pair from a drawer with one odd tripleEasy
  14. Mixed equilibrium in a distance game on [0,1]Medium
  15. Three dice with a maximum of exactly fourMedium
  16. Equal tail counts in two sets of four tossesEasy
  17. Conditioning a normal on the radius squaredMedium
  18. Die rolls that continue on even faces and headsEasy
  19. Two boys given a boy born on a FridayMedium
  20. Expected uniform draws until the sum passes 2Hard
  21. Rolls until neighbouring faces appear in a rowMedium
  22. Cash out the last roll or risk a sixEasy
  23. Being dealt two acesEasy
  24. Marble box game with payoffs that shrinkHard
  25. Guessing the rank of one revealed uniformMedium
  26. Waiting for a decreasing run to breakMedium
  27. Which comes first, HTH or HHTMedium
  28. Random walk on a 100-point circleMedium
  29. Correlation of sum and difference under rho of -1Medium
  30. First coin toss still ahead after ten tossesMedium
  31. Biased walk with up-probability one third reaching 7Easy
  32. Most regions cut out by ten linesMedium
  33. Splitting black and white balls between two urnsEasy
  34. Lowest common correlation for seven variablesMedium
  35. Two walkers crossing a 4 by 4 grid meetingMedium
  36. Average card value when hearts count doubleEasy
  37. Next draw yellow after red leads by fiveMedium
  38. Point in a triangle making a small sub-triangleMedium
  39. Random point in a cylinder lying in its coneEasy
  40. Heads in five tosses when the ends disagreeEasy
  41. Even row and column sums in a 3 by 3 gridMedium
  42. Variance of the longer piece of a cut ropeMedium
  43. Noisy yes or no message passed down a long chainMedium
  44. Only the number seven left unchosenMedium
  45. Odd dot product of two random 0-1 vectorsMedium
  46. Counting solutions with a sum between 6 and 10Hard
  47. Rolling a d10 until the lcm passes 2000Hard
  48. Expected time for an upward-biased walk to gain 1Medium
  49. Hopping up ten stairs in an even number of jumpsEasy
  50. Blue socks needed for an even chance of a red pairEasy