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Interview prep / Probability

Probability interview questions: page 18 of 19

Questions 851–900

  1. All random points on a circle in one halfMedium
  2. Odds of quads, a full house and two pairEasy
  3. Locks and keys so any six of eleven can openHard
  4. Players ranked first and second meeting in the finalMedium
  5. Five letters, none in its own envelopeMedium
  6. Chance a random cube has last two digits 11Medium
  7. Both children boys given at least one sonEasy
  8. Two sons given the child you happened to meetEasy
  9. Double-headed coin among a thousand after ten headsEasy
  10. Fair 50-50 outcome from a coin of unknown biasEasy
  11. Third throw landing farther out than the firstMedium
  12. Best queue position for a shared-birthday prizeMedium
  13. Three successive dice coming up strictly ascendingEasy
  14. Extinction probability for a splitting amoebaMedium
  15. Red candies running out before blue and greenHard
  16. Alternating tosses: first to complete heads then tailsMedium
  17. Going first or second with one bullet and no respinEasy
  18. Roulette with a respin before every trigger pullEasy
  19. To respin or not with two randomly loaded chambersEasy
  20. Each bridge hand receiving exactly one aceMedium
  21. Chance of reaching N before going brokeMedium
  22. Shooting where success rate equals past hit fractionHard
  23. Seeing a car in 5 minutes from the 20-minute oddsEasy
  24. Expected wait and time since the last Poisson busMedium
  25. First four raw moments of a standard normalEasy
  26. Expected loops from tying 100 noodle endsMedium
  27. Die payouts that continue only on high rollsEasy
  28. How deep in the deck the first ace appearsMedium
  29. Chance n uniforms add up to at most oneMedium
  30. Bounds on joint default of two bondsMedium
  31. Distribution of the largest and smallest uniformsEasy
  32. Correlation between min and max of two uniformsHard
  33. Five hundred bouncing ants on a one-foot stringHard
  34. Ruin game with a favourable two-thirds edgeMedium
  35. A twelve versus back-to-back sevens with two diceMedium
  36. Waiting times for HHT and for THHMedium
  37. Which comes first, HHT or THHMedium
  38. Choosing first or second in a triplet raceHard
  39. Repainting balls until a single colour remainsHard
  40. Random walker on a 100-metre bridgeMedium
  41. Collect die faces until a four or higherEasy
  42. Queue for five-dollar tickets with no changeHard
  43. Expected flips for a streak of n headsMedium
  44. Optimal stopping with up to three die rollsMedium
  45. Hedging a series bet with single-game wagersHard
  46. When to stop a die game where a six wipes you outHard
  47. Stopping rule for a red-black card payoff gameHard
  48. Winning with any probability using a fair coinMedium
  49. Central limit theorem and why it matters in financeEasy
  50. Jensen's inequality and convexity in pricingEasy