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A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :

Options

  1. A63 925
  2. B17 231
  3. C16 231
  4. D64 925

Correct answer

C. 16 231

Step-by-step solution

The probability that the first pair drawn consists of one blue and one green ball is: P₁ = ⁶C₁ ⁶C₁ ¹²C₂ = 36 66 = 6 11 Since the balls are drawn without replacement, 5 blue and 5 green balls remain. The probability that the second pair consists of one blue and one green ball is: P₂ = ⁵C₁ ⁵C₁ ¹⁰C₂ = 25 45 = 5 9 Continuing this process for all 6 pairs, the probabilities are: P₃ = ⁴C₁ ⁴C₁ ⁸C₂ = 16 28 = 4 7 P₄ = ³C₁ ³C₁ ⁶C₂ = 9 15 = 3 5 P₅ = ²C₁ ²C₁ ⁴C₂ = 4 6 = 2 3 P₆ = ¹C₁ ¹C₁ ²C₂ = 1 1 = 1 The required probability is

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