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Interview prep / Probability

Probability interview questions: page 17 of 19

Questions 801–850

  1. Making one-third and two-thirds events from a coinEasy
  2. Payout from rerolling a die until it shows above oneEasy
  3. Both of the first two cards dealt are kingsEasy
  4. Weakest gunman's best opening move in a truelHard
  5. Last-second shot choice when trailing by twoEasy
  6. Paying 1.50 dollars to spin a five-slot wheelEasy
  7. Is 10-to-1 enough for picking four winnersEasy
  8. Two named cards before a third among fourEasy
  9. Mean of e to a zero-mean normalEasy
  10. One huge die payout versus a million tiny onesEasy
  11. Posterior disease probability after a positive screenEasy
  12. Splitting 20 thousand dollars among five fundsEasy
  13. How many chips so every cookie gets oneHard
  14. Die game that banks on four or five, busts on sixMedium
  15. Average longest piece of a stick cut twiceHard
  16. Entry fee for a game paying one die faceEasy
  17. Pay-per-box hunt for a hidden prizeEasy
  18. Value of guessing a number that pays itselfHard
  19. Expected wealth when heads doubles and tails halvesMedium
  20. Mean and variance of the wait for headsEasy
  21. Flipping until two successive results agreeEasy
  22. Waiting times for one head and for HH with biasMedium
  23. Spotting a two-headed coin after three headsEasy
  24. Next toss after a streak from an ordinary coinMedium
  25. Counting HHHHHHTTTTTT runs in a million flipsMedium
  26. Sex of the other baby when one is a girlEasy
  27. Two girls given various clues about the daughtersHard
  28. Odds the fourth weekday of a month is ThursdayEasy
  29. First card outranking the second card drawnEasy
  30. Knockout bracket where the two best teams collide lastMedium
  31. Matching pair from two red and two black socksEasy
  32. Drawing two aces with and without putting backEasy
  33. Mean return time of a random walk on a cubeMedium
  34. Survival odds on a plank with sharks at one endEasy
  35. Can corr(A,C) be 0.1 given the other twoMedium
  36. Cumulative distribution of a uniform on an intervalEasy
  37. Expected largest value and spread of n uniformsMedium
  38. A distribution whose variance is infiniteEasy
  39. Change-of-variables formula for a densityEasy
  40. CDF and density of the kth smallest of n drawsMedium
  41. Density of the sum of two independent uniformsEasy
  42. Statement of the classical CLTEasy
  43. Why a covariance matrix is positive semi-definiteMedium
  44. Second moment and MGF of a GaussianEasy
  45. Average value of Phi at a standard normal drawEasy
  46. Symmetric walk from 80 absorbed at 0 or 1000Easy
  47. Splitting black and white balls between two sacksEasy
  48. Mean of a standard normal given it is positiveEasy
  49. One extra coin: chance of out-heading the opponentMedium
  50. Beating the dealer with a strictly higher cardEasy