Multiple choice

Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: 5 balls are drawn at random from a bag which contains 10 white, 7 blue and 13 red balls. What is the probability if two balls are red? Quantity II: 7 marbles are drawn at random from a jar which contains 8 brown marbles, 6 blue marbles and 7 grey marbles. Find the probability if at least 4 marbles are brown.

  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: Probability of exactly 2 red out of 5 from 10W, 7B, 13R (30 total) = C(13,2)×C(17,3)/C(30,5) = (78 × 680)/142506 ≈ 0.372. Quantity II: Probability of at least 4 brown out of 7 from 8 brown, 6 blue, 7 grey (21 total). This is complex to calculate but involves finding P(4 brown) + P(5 brown) + P(6 brown) + P(7 brown). The probability of getting 4 or more from only 8 browns in a sample of 7 from 21 total is relatively small. 0.372 > small probability, so Quantity I > Quantity II.

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