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Interview prep / Probability

Probability interview questions: page 11 of 19

Questions 501–550

  1. Safe coin bias when the opponent chooses secondMedium
  2. Rolls of a five-sided die to reach a total of fiveHard
  3. Variance of the time for a drifting walk to reach 7Medium
  4. Second seed surviving ten rounds of winner-staysMedium
  5. One max of exponentials beating twice anotherMedium
  6. Recovering beta parameters from a scaled variableMedium
  7. Leading candidate never trailing in a 100 to 80 countHard
  8. Two random points on a square's edge over unit apartMedium
  9. d30 against a d20 with one optional rerollMedium
  10. Even outcome after shaving a pip off a random faceEasy
  11. Round table on three randomly placed legsHard
  12. Point sequences reaching four all in a tennis gameEasy
  13. Expected squared distance after 16 random unit stepsMedium
  14. Which shelf given two grey socks drawnEasy
  15. Expected distinct colours in a three-candy grabEasy
  16. Waiting time for a win with shrinking oddsEasy
  17. Scheduling five students into fifteen slotsEasy
  18. Integral of x times a stretched exponentialEasy
  19. Bayes update on a performer's home cityEasy
  20. Pull again or add a bullet and spinMedium
  21. Paying for extra uniform draws to raise the maxHard
  22. Last queen before last king given an early patternEasy
  23. Variance of fixed minus non-fixed pointsHard
  24. Draws needed to clear a deck of ten pairsMedium
  25. Keep or pay to discard cards for an average payoutEasy
  26. Scaled chance three uniform integers sum to NMedium
  27. Arrangements of 19 balls in three coloursEasy
  28. Adding up every multinomial coefficient of order 7Medium
  29. Last passenger's seat after a random first pickMedium
  30. Correlation between counts of ones and fivesMedium
  31. Random walk exiting a 4 by 4 square sidewaysEasy
  32. Top seed meeting the third-best player in the finalMedium
  33. Extinction chance when each cell has up to three offspringMedium
  34. No two neighbouring lights on in a 3 by 3 gridMedium
  35. Orders for breaking stacked targets column by columnEasy
  36. Random circle lying fully inside a squareMedium
  37. Complete sock pairs left after drawing eightMedium
  38. Same colour from two different jarsEasy
  39. Painted cube piece showing five blank facesMedium
  40. Paying a dollar to reflip four coinsMedium
  41. Expected position of the final heart in a shuffled deckMedium
  42. Even sum of four primes chosen from the first sixteenEasy
  43. Shares of a second stock minimising portfolio varianceEasy
  44. Mean plus variance of rug repair costEasy
  45. Expected product of coordinates in the unit discEasy
  46. Average wait for a bus every ten minutesEasy
  47. Top three of five dice summing to 18Easy
  48. Posterior mean of a coin with a Beta(10,10) priorMedium
  49. Exactly one head given at least one in three tossesEasy
  50. Parity of the running total until a six appearsMedium