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Interview prep / Probability

Probability interview questions: page 5 of 19

Questions 201–250

  1. CLT for the gap between two Beta(1,2) sumsEasy
  2. Even or odd bets offered by a genieEasy
  3. Fair prize for five cards dealt in sorted orderEasy
  4. Ordered triples of positive integers summing to 25Easy
  5. A run of exactly three heads in six tossesEasy
  6. Rotation-distinct rings of three red, three blueEasy
  7. Next step of a walk conditioned to hit 7Medium
  8. Two blue birds side by side on a wireEasy
  9. Spouses landing together in a random pairingEasy
  10. Beating the dealer with one card eachMedium
  11. Bayesian update from one slip drawn from a boxMedium
  12. Head density in tosses with no two heads adjacentHard
  13. Expected head fraction when stopping once aheadHard
  14. Exactly two aces in a thirteen-card handEasy
  15. Expected hitting time of +1 for a fair walkMedium
  16. Ten-door Monty Hall with three goats revealedMedium
  17. Expected rope profit with Poisson defectsEasy
  18. Implied scale of an exponential from an option priceMedium
  19. Random point on a snowman below 39 inchesEasy
  20. Ratio of a 3-5-4-4 split to an even splitEasy
  21. Two random subsets of five elements overlappingHard
  22. Correlation of sum and difference of linked variablesMedium
  23. Conditional ordering of three iid uniformsEasy
  24. Odd-only subsets with two of 1, 2, 3Easy
  25. Choosing a radius in a laser-pointer betEasy
  26. Chip 12 going to the second playerEasy
  27. Revolver with one bullet and no re-spinMedium
  28. Gift baskets with a random number of item typesMedium
  29. Four of a kind given at least three of a kindEasy
  30. Four dice adding up to twentyEasy
  31. Order of chess opponents to win two in a rowMedium
  32. Standard deviation of a shop's daily pizza outputEasy
  33. Smallest class where a shared birthday is likelyMedium
  34. Boy-girl neighbours in a random line of 25Medium
  35. One uniform beating three othersEasy
  36. Couples adjacent at an alternating round tableMedium
  37. First to make the running total divisible by 7Easy
  38. Covariance of a squared radius and its complementEasy
  39. Seven people seated round a table in age orderEasy
  40. Mean gap between thank-you cards from two firmsMedium
  41. When the final of four bulbs failsMedium
  42. 22 coins against 20: who gets more headsMedium
  43. Mean distance between two random points on a circleHard
  44. Subsets of 1 to 10 with a single adjacent pairHard
  45. Emptying the bowl when red cherries run outMedium
  46. Random lattice descent from (4,4) hitting the originMedium
  47. Random split of 50 nuggets among four studentsMedium
  48. Dice total divided by the better of two diceMedium
  49. Best spot in line on a glass-tile bridgeEasy
  50. Random unit cube from a painted 5x5x5 blockEasy