Question
A bag contains 4 yellow, 5 black and 7 white flowers.
Three flowers are drawn randomly. Quantity I: What is the probability that all three flowers are of white colour? Quantity II: What is the probability that all three flowers are of different colour? In each of the following questions, read the given statements and compare the two given quantities on it basis. Give answer:Solution
Quantity I: n(s) = ¹⁶C₃ = (16 × 15 × 14)/(3 × 2 × 1) = 560 n(E) = ⁷C₃ = (7 × 6 × 5)/(3 × 2 × 1) = 35 P(E) = 35/560 = 35/560 = 1/16 Quantity II. n(s) = ¹⁶C₃ = (16 × 15 × 14)/(3 × 2 × 1) = 560 n(E) = ⁴C₁ × ⁵C₁ × ⁷C₁ P(E) = 140/560 = 1/4 Hence, Quantity I < Quantity II
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