Multiple choice

Find the value of quantities and state the correct relationship.\newline In a container there are 20 eggs out of which 5 are rotten. Two eggs are chosen at random.\newline Quantity I: Probability that at least one egg is rotten\newline Quantity II: Average of (\frac{1}{2}), (\frac{1}{3}) and (\frac{1}{5})

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
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A Correct answer
Explanation

Quantity I: Probability at least one rotten = 1 - P(both good) = 1 - (15C2/20C2) = 1 - (105/190) = 85/190 = 17/38 ≈ 0.447. Quantity II: Average of 1/2, 1/3, 1/5 = (1/2 + 1/3 + 1/5)/3 = (15/30 + 10/30 + 6/30)/3 = (31/30)/3 = 31/90 ≈ 0.344. Since 17/38 > 31/90, Quantity I > Quantity II.

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