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: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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