Skip to content
Interview prep / Probability

Probability interview questions: page 14 of 19

Questions 651–700

  1. Keep or reroll with a penalty when the total hits sevenMedium
  2. One hundred random circle points in a semicircleMedium
  3. First return to equal heads and tails with a biased coinHard
  4. Seeing 1, 3 and 5 before any even rollEasy
  5. Subsets where each chosen letter may be marked boldEasy
  6. Variance of a Monte Carlo quarter-circle pi estimateMedium
  7. Optimal mix of deposits and withdrawals over 100 turnsHard
  8. Variance of the limit of randomly halved intervalsMedium
  9. Crash probability in half an hour from the hourly rateEasy
  10. Most likely square for a one-or-two jumping frogMedium
  11. Fair value of a die with up to three rollsMedium
  12. Loaded die parameter maximising a total of sevenEasy
  13. Red probability on draw 11 when black turns redMedium
  14. Five random intervals sharing a common pointHard
  15. Matching pair from ten differently coloured sock pairsEasy
  16. Expected tosses until three identical faces in a rowMedium
  17. All six songs of one artist before the second of anotherEasy
  18. Expected regions cut by two random chordsMedium
  19. Even stopping time for a first repeated faceEasy
  20. Chance one bubble sort pass fully sorts 100 itemsMedium
  21. Top two seeds meeting in a 128-player finalMedium
  22. Second seed upsetting the top seed in a 16-player finalMedium
  23. Value of rolling until something other than a oneEasy
  24. Expected return time of a random walk on a cubeMedium
  25. Rounds of two dice needed to see every faceMedium
  26. Multiplier making a stop-anytime die game fairEasy
  27. Weight minimising variance of a blend of two variablesEasy
  28. First HH completed exactly on toss tenMedium
  29. Stopping a deal to bet the next card is redMedium
  30. Three ants on a triangle avoiding a shared cornerEasy
  31. Expected colour runs drawing 50 red and 50 blueHard
  32. Sum of 100 hundred-sided dice divisible by 100Medium
  33. Value of a call on a drilling outcome stockEasy
  34. Most heads when coins can only be turned in pairsEasy
  35. Gain from respinning the revolver in two-bullet rouletteEasy
  36. Matching-integer game paying the square of the numberMedium
  37. Total of five appearing before a total of twoEasy
  38. One extra coin and the chance of more headsEasy
  39. Two cuts on opposite halves farther apart than a thirdMedium
  40. Rerolling three dice to get the same multisetMedium
  41. Log of the limiting fraction of empty binsMedium
  42. Payout from blue beating red by three before a tieEasy
  43. Paid redraws from a hat numbered 1 to 100Hard
  44. Normal approximation to total weight above 26 kgEasy
  45. Die game paying a dollar per low roll until it endsMedium
  46. First to have tossed both faces wins with alternating turnsEasy
  47. Conditional mean of one normal given the sumMedium
  48. Distinct numberings of a cube up to rotationMedium
  49. Expected bills drawn to post bail with half fakesMedium
  50. Expected number of long cycles in a random permutationHard