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CUET · MATHS · PYQ PAPER 2025

Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag is selected at random and then a ball is drawn from it. The probability that the ball drawn is black is :

  1. A \(\frac{7}{15}\)
  2. B \(\frac{11}{15}\)
  3. C \(\frac{14}{15}\)
  4. D \(\frac{13}{15}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{7}{15}\)

Step-by-step Solution

Detailed explanation

\(P(B) = P(B|Bag\ I) \cdot P(Bag\ I) + P(B|Bag\ II) \cdot P(Bag\ II)\) \(P(B) = \frac{3}{5} \cdot \frac{1}{2} + \frac{2}{6} \cdot \frac{1}{2}\) \(P(B) = \frac{3}{10} + \frac{1}{6}\) \(P(B) = \frac{9}{30} + \frac{5}{30}\) \(P(B) = \frac{14}{30} = \frac{7}{15}\)