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Interview prep / Probability

Probability interview questions: page 7 of 19

Questions 301–350

  1. Arrangements of BOOLAHUBBOO with B's firstMedium
  2. Russian roulette with a re-spin, going secondMedium
  3. Examining goats until both sexes have appearedEasy
  4. Who gets the first head with a one-third coinMedium
  5. When to stop drawing from 2 white and 3 blackMedium
  6. First multiple of 77 at or above 700000Easy
  7. Expectation of X over Y plus 1 for a joint densityMedium
  8. Orange ball after moving 300 balls between urnsMedium
  9. Pan holding the 206 gram weight tipping downEasy
  10. Die roll payout with one optional rerollEasy
  11. Pair among three socks from ten colour pairsEasy
  12. Guessing a deck of three aces and three jacksMedium
  13. How many searchers to hire for a lost driveMedium
  14. Stopping threshold in continuous blackjackHard
  15. Winning a tennis game from 30 allMedium
  16. Paying to roll a d20 more times for its maximumHard
  17. Expected share of the first half of a sumEasy
  18. Seven-digit codes with non-decreasing digitsMedium
  19. Purple cherries left when the last red is eatenMedium
  20. Two people picking the same triangle from 8 pointsEasy
  21. Fair coin betting between 1000 and 500 dollarsEasy
  22. Last shiny penny arriving after the fourth drawEasy
  23. One king, queen and jack before the two of heartsMedium
  24. Choosing die sizes when the sum must stay under 8Medium
  25. Even gaps between six pairs of coloured blocksMedium
  26. Variance of a normal with random mean and scaleMedium
  27. Waiting to beat a random Beta thresholdMedium
  28. Red cherry after moving one between bowlsEasy
  29. Group size maximising expected unshared birthdaysMedium
  30. Reaching a two-point lead with a 30 percent edgeEasy
  31. Two random breaks giving triangle sidesHard
  32. Rolls of a d12 until an odd number appearsEasy
  33. Counting rectangles on an 8 by 8 boardMedium
  34. Uniform samples needed to hit a small windowMedium
  35. One random subset contained in anotherHard
  36. Down-biased walk ever reaching plus oneMedium
  37. Repeating the same pair of dice valuesEasy
  38. Team assignments with two marketing refusalsEasy
  39. Back-to-back heads with coins of bias 1 over kEasy
  40. Darts needed for a 90 percent bullseye chanceEasy
  41. Expected peak of an increasing run of uniformsHard
  42. Coordinate variance in a 10-dimensional ballHard
  43. Each player dealt one king, queen and jackMedium
  44. Meeting when arrivals are uniform on different windowsMedium
  45. Stacking 1-high and 2-high blocks to height 12Easy
  46. Allocating 50 million across five asset classesEasy
  47. Expected top rank among four dealt cardsMedium
  48. Dice total of 4 showing up before a 2Easy
  49. Two draws with replacement paying five times faceEasy
  50. 101 uniforms all at least 0.001 apartHard