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    Question

    An urn contains 3 green, 5 blue, 6 black and 4 yellow

    marbles. Quantity I – If two marbles are picked at random, what is the probability that both are green? Quantity II – If three marbles are picked at random, what is the probability that two are blue and one is yellow? In each of the following questions, read the following questions, read the given statements and compare given two quantities on its basis:
    A Quantity I > Quantity II Correct Answer Incorrect Answer
    B Quantity I < Quantity II Correct Answer Incorrect Answer
    C Quantity I ≥ Quantity II Correct Answer Incorrect Answer
    D Quantity I ≤ Quantity II Correct Answer Incorrect Answer
    E Quantity I = Quantity II Correct Answer Incorrect Answer

    Solution

    Quantity I : Total no. of marbles in the urn = 3 + 5 + 6 + 4 = 18 P(S) = ¹⁸C₂ = (18 ×17 )/(2 × 1) = 153 P(E) = ³C₂ = 3 ∴ Required probability = 3/153 = 1/51 Quantity II : Total no. of marbles in the urn = 3 + 5 + 6 + 4 = 18 P(S) = ¹⁸C₃ = (18 ×17 ×16 )/(3 × 2 × 1) = 816 P(E) = ⁵C₂ × ⁴C₁ = (5 × 4)/2 × 4 = 40 ∴ Required probability = 40/816 = 5/102 ∴ Quantity I < Quantity II.

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