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    Question

    In each of the following questions, read the following questions, read the given statements and compare given two quantities on its basis:

    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?

    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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