Multiple choice

Each question contains a statement followed by Quantity I and Quantity II. Read the contents clearly and answer your questions accordingly. \begin{enumerate} \item A bag contains 7 black pens, 5 pink pens and 4 yellow pens. \item Quantity I: If 3 pens are drawn randomly, then find the probability of getting at least one pink pen? \item Quantity II: If 2 pens are drawn randomly, then find the probability of getting both the pens is either black or yellow?\end{enumerate}

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: P(at least 1 pink) = 1 - P(no pink) = 1 - (11C3/16C3) = 1 - 165/560 = 395/560 = 79/112 ≈ 0.705. Quantity II: P(both black or yellow) = 11C2/16C2 = 55/120 = 11/24 ≈ 0.458. Cross-multiplying: 79*24 = 1896, 112*11 = 1232. Since 1896 > 1232, Quantity I (79/112) > Quantity II (11/24). Option C is correct.

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