Multiple choice

Find the correct relationship between given quantities. Quantity I- A bag contains 3 green, 2 yellow and 3 purple balls. Two balls are drawn at random, what is the probability that no ball is purple. Quantity II- A bag contain 4 red balls and 6 yellow balls.If three balls are picked randomly then what is the probability that they are of the same color.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
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A Correct answer
Explanation

Quantity I: P(no purple) = C(5,2)/C(8,2) = 10/28 = 5/14 ≈ 0.357. Quantity II: P(all same color) = P(all red) + P(all yellow) = C(4,3)/C(10,3) + C(6,3)/C(10,3) = 4/120 + 20/120 = 24/120 = 1/5 = 0.2. Since 0.357 > 0.2, Quantity I > Quantity II.

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