Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II.You have to find the correct relationship. A box contains 12 black balls, 15 green balls, 13 yellow balls and 16 purple balls. Quantity I: If three balls are drawn at random then the probability that all the balls are either green or yellow. Quantity II: If three balls are drawn at random then the probability that all are of different colours.

  1. Quantity I ≤ Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I < Quantity II

  5. Quantity I = Quantity II, or relation cannot be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 56. Quantity I: (15C3 + 13C3)/56C3 = (455 + 286)/56C3 = 741/327600 ≈ 0.00226. Quantity II: Different colors means one from each color. P = (12C1 × 15C1 × 13C1 × 16C0)/56C3... This calculates to approximately 0.116. Therefore Quantity II > Quantity I.

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