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Interview prep / Probability

Probability interview questions: page 10 of 19

Questions 451–500

  1. Variance of a standard uniform variableEasy
  2. Keep an 8-sided roll or switch to a d12Easy
  3. Feasible correlation range for a third pairMedium
  4. Most throws keeping a small-sum chance under halfEasy
  5. Final length of a die sequence with resetsHard
  6. Top two seeds meeting in a king-of-the-hill finalEasy
  7. Penalty streak with success rate equal to past rateHard
  8. Fair entry fee per door when hunting a prizeEasy
  9. Re-flipping tails only in pairs with four coinsMedium
  10. Second pair from a 40-card deck missing a pairEasy
  11. First matching sock pair arriving on day threeMedium
  12. Crossings in a random closed polygon in a circleHard
  13. Corner cube given a red face on a painted cubeMedium
  14. Forgetful singer restarting a countdown songHard
  15. Average number of closed groups from a name drawHard
  16. Expected perimeter of a triangle inscribed at randomHard
  17. Small dice total given two or more even facesEasy
  18. Expected number of visible heads in a queue of 20Easy
  19. Specific coin order given three heads in fiveEasy
  20. Alternating tosses race to a second headMedium
  21. Two numbers landing in different random groupsEasy
  22. Late lecturer making a mile in random dashesMedium
  23. Random wire joins forming one 10-mile loopMedium
  24. Expected return of a three-asset equal-weight mixEasy
  25. Triangle from a fixed loaf and a randomly cut oneEasy
  26. Uniforms needed to exceed the log of twoHard
  27. Difference of normals exceeding a third normalEasy
  28. Counting pure equilibria in a sealed coin-chest auctionHard
  29. Boxes needed to collect five equally likely prizesMedium
  30. Weighted sum of uniforms until the first riseHard
  31. First toss heads given no two heads in a rowMedium
  32. Setting a coin bias to make a first-head race fairMedium
  33. Letter location after an unproductive mailbox checkEasy
  34. Balanced strings using two kinds of bracketsMedium
  35. Chance of a full house in five cardsMedium
  36. Expected largest label among ten drawn from twentyMedium
  37. Best guess of 100 tosses after one yes-no queryMedium
  38. Four cards drawn coming out in increasing orderEasy
  39. Mean distance of a random dart from the centreEasy
  40. Overlap of two random intervals in the unit lineMedium
  41. Variance of first passage time for a biased walkMedium
  42. Matching tail counts in two blocks of tossesEasy
  43. Expected disjoint blocks of five black cellsHard
  44. Capped doubling payout from tossing until headsMedium
  45. A run of exactly three heads in six tossesEasy
  46. Mean gap between two uniforms on three to fourEasy
  47. Expected painted faces on a random unit cubeMedium
  48. Expected colour runs in a biased row of 25 cellsMedium
  49. One random number strictly topping anotherMedium
  50. Bear fishing until three catches, fifth attemptEasy