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Interview prep / Probability

Probability interview questions: page 13 of 19

Questions 601–650

  1. Best place in a queue for a birthday-match prizeHard
  2. Rolls needed for back-to-back sixesEasy
  3. Race between a second five and seeing both four and sixMedium
  4. Mean return time for a random walk on cube cornersMedium
  5. Ordering three second-moment quantities for diceMedium
  6. Target surviving a randomly placed blastEasy
  7. Family size making two gender events independentEasy
  8. No empty box after a geometric number of ballsHard
  9. Odds against a four of a kind in five cardsEasy
  10. Tossing until heads and tails are levelHard
  11. Expected tosses for the winner of a first-head raceHard
  12. Back where he started after nine random movesEasy
  13. Switching doors after a random goat revealMedium
  14. Expected middle value of three diceEasy
  15. Small loaves eaten before all large loaves are halvedHard
  16. Coin thickness for a one-in-three edge landingHard
  17. First uniform draw that is not a running maximumMedium
  18. Chance the top two cards share a rankEasy
  19. Chebyshev bound on total weight of 100 cheese blocksEasy
  20. Expected ratio of partial sums S40 over S20Medium
  21. Ways to climb ten stairs in hops of one or twoMedium
  22. Equal-profit bets across three match outcomesEasy
  23. Best stopping card for an ace-placement prizeHard
  24. Two players with four dollars each after eight tossesMedium
  25. Expected boys seated given a single-gender trioEasy
  26. Solving for the takeover price from a call valueEasy
  27. Second red draw from a random urn as urns multiplyHard
  28. Bayes update on a witness naming a traderEasy
  29. Largest variance for a variable bounded in minus one to oneMedium
  30. Number of winning lines in 4x4x4 noughts and crossesMedium
  31. Fraction of diners who know a seat neighbourMedium
  32. Expected wait for the next bad day in a two-state chainEasy
  33. Subsets of 1 to 10 with two of the first threeEasy
  34. Distinct monomials in a six-variable sum to the 18thMedium
  35. Rug flaws on three square yards in exponential formEasy
  36. Probability X is positive given X plus Y is positiveMedium
  37. Expected value of a two-coin win-two lose-seven gameEasy
  38. Random inscribed triangle containing the centreHard
  39. Coin bias making a tie as likely as one player winningEasy
  40. Mean painted faces on a unit cube from a 10x20x30 blockMedium
  41. Product of two uniforms exceeding one halfEasy
  42. Whether gladiator matchup order matters for BobHard
  43. Expected tosses until heads lead by 10 or trail by 7Easy
  44. Max heads when you may reflip coins two at a timeEasy
  45. Splitting good and bad sweets between two boxesEasy
  46. Covariance between a standard normal and its squareEasy
  47. Shortest of three random pieces under five centimetresHard
  48. Correlation after opposite-sign linear transformsEasy
  49. Chance of the exact pattern HTHT in four tossesEasy
  50. Break-even loss in a double-six versus single-six gameEasy