Multiple choice

In the given questions, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option: Quantity I: A box contains 4 blue pens, and 5 green pens and 6 red pens. Two pens are drawn at random from the box. What is the probability that the ball drawn is either red or green? Quantity II: A box contains 4 blue pens, and 5 green pens and 6 red pens. Two pens are drawn at random from the box. What is the probability that the ball drawn is either blue or green?

  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 no relation
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A Correct answer
Explanation

Quantity I: P(red or green) = (6C2 + 5C2 + 6C1*5C1)/15C2 = (15 + 10 + 30)/105 = 55/105 = 11/21 ≈ 0.524. Quantity II: P(blue or green) = (4C2 + 5C2 + 4C1*5C1)/15C2 = (6 + 10 + 20)/105 = 36/105 = 12/35 ≈ 0.343. Since 11/21 > 12/35, Quantity I > Quantity II is correct.

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