The Interview Guide for Quants and Traders

The Interview Guide for Quants and Traders

Probability and Statistics Questions

  1. 90 Cents Please
  2. Aces for All
  3. Any Cake Left
  4. Chessboard Crossing
  5. Choosing Blocks
  6. Coins Race #2
  7. Democratic Safe
  8. Dice Order
  9. Flipping a Coin #1
  10. Flipping a Coin #2
  11. Lights On #1
  12. Lights On #2
  13. Lights On #3
  14. Maximum Intersections
  15. Meeting Your Friend
  16. Overbooked Flight
  17. Poker – Four of a Kind
  18. Poker – Full House
  19. Poker – Two Pair
  20. Running Rabbit
  21. Sequences
  22. Specific Card #2
  23. Specific Card #3
  24. Stock Price Coin Flip
  25. Sum of Primes
  26. Sum to 3
  27. Table of Ages
  28. Algorithms
  29. Child's Gender
  30. Coin Toss
  31. Dart Game
  32. Favorite Sports
  33. First to Heads
  34. Games Store
  35. Hospital
  36. Monty Hall Problem
  37. Painted Cube
  38. Racing
  39. Russian Roulette #1
  40. Russian Roulette #2
  41. Russian Roulette #3
  42. Russian Roulette #4
  43. Second Heads
  44. Unfair Heads #1
  45. Unfair Heads #2
  46. Vacant Room
  47. Which Die Was It
  48. 100-Sided Die
  49. 5 Descending Cards
  50. Basketball Practice #1
  51. Basketball Practice #2
  52. Cards in Bin
  53. Company Acquired or Not
  54. Dice Game
  55. Dice Sum
  56. Dice With Same Numbers
  57. Divisible Throws
  58. Double Down Coin Bet
  59. Drunk Student #1
  60. Drunk Student #2
  61. Empty Boxes
  62. Exponential Distribution #1
  63. First Ace
  64. First Flip Wins
  65. Flip 100 Coins
  66. Flip 4 coins #1
  67. Free Ticket
  68. Gameshow Stop or Go
  69. Kelly Betting #1
  70. Kelly Betting #2
  71. Other Than Six
  72. Repeating Dice
  73. Shooting Star
  74. Specific Card #1
  75. Sum Two Dice
  76. Three Blue Orbs
  77. Throw a 6 #1
  78. Throw a 6 #2
  79. Throw a 6 #3
  80. Throw a 6 #4
  81. Throw Until Match
  82. Toy Collection #1
  83. Toy Collection #2
  84. Two Same Dice
  85. Uniform Distribution #1
  86. All Faces
  87. All-Boy City
  88. Bikes on Road
  89. Birthday Problem #1
  90. Birthday Problem #2
  91. Both Card Colors
  92. Checkmate
  93. Coins in Boxes
  94. Coins Race #1
  95. Complementary
  96. Even Heads
  97. Even Sum
  98. Exponential Distribution #2
  99. Five Ascending Cards
  100. Gambler's Ruin
  101. Going to the Beach #2
  102. Higher Card
  103. Jumping Robots
  104. Knockout Stage
  105. Lower Die
  106. Meeting Probability
  107. Multiply 3 Dice
  108. Old Phone #1
  109. Old Phone #2
  110. Optimal Spread
  111. Outcome Dice
  112. Perfect Correlation
  113. Rainy Day
  114. Tennis Game
  115. The Highest Six
  116. Uniform Distribution #2
  117. Uniform Distribution #3
  118. Uniformly Distributed Profit
  119. Variance of Two Variables
  120. Walking Home #1
  121. Walking Home #2
  122. Win in 2 or 3 Sets
  123. Animal Migations
  124. Bankrupt
  125. Coin Series #1
  126. Coin Series #2
  127. Coin Series #3
  128. Dominant Game
  129. Jumping Toad
  130. Parking Meter
  131. Random Ant
  132. Region Spinner
  133. The Drunkard's Walk
  134. Top 2000 Songs
  135. Beat the Odds
  136. Parimutuel Betting
  137. Tennis Odds
  1. Combinatorial Analysis
  2. Conditional Probability
  3. Expected Value
  4. General
  5. Markov Chain Probability
  6. Game Puzzle
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90 Cents Please

Viktor has to buy some milk. The farmer asks 90 cents for the milk. Viktor knows that he has the following coins in his pocket, one of each coin: 2 euros, 1 euro, 50 cents, 20 cents, 10 cents, 5 cents, 2 cents, 1 cent. What is the probability that – if he grabs three random coins from his pocket – the total value will be 90 cents or higher?

Hint

Use combinatorial analysis. Start with the two euros coin and iterate down to lower value coins.

Answer

Viktor is able to make Quicklatex. Com a80ee9a9df111a2fe100c353bcca8458 l3 distinct combinations with 8 coins.
  • If the two euros coin is involved, it doesn’t matter what the other coins are. So, Quicklatex. Com a9bb4068057688ad63230d28c9859737 l3 combinations are sufficient to pay for the milk.
  • If the one euro coin is involved, another Quicklatex. Com 7f9e79aa3781b2b9768ecc25f9eddf7d l3 combinations are already sufficient to pay for the milk.
  • If the two- and one euro coin are both not involved, then we can’t find a combination that’s 90 cents or higher.
So, a total of 36 combinations is sufficient to pay for the milk, out of the 56 possible combinations. Therefore, the probability that Viktor will be able to pay for the milk by grabbing three random coins from his pocket is 36/56.