ExamBro
ExamBro
AP EAMCET · Maths · Probability

A bag P contains 4 red and 5 black balls, another bag Q contains 3 red and 6 black balls. If one ball is drawn at random from bag \(P\) and two balls are drawn from bag Q, then the probability that out of the three balls drawn two are black and one is red, is

  1. A \(\frac{25}{64}\)
  2. B \(\frac{25}{64}\)
  3. C \(\frac{27}{64}\)
  4. D \(\frac{35}{54}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{25}{64}\)

Step-by-step Solution

Detailed explanation

\(P(\text{1R from P, 2B from Q}) = \frac{4}{9} \times \frac{\binom{6}{2}}{\binom{9}{2}}\) \(P(\text{1R from P, 2B from Q}) = \frac{4}{9} \times \frac{15}{36} = \frac{4}{9} \times \frac{5}{12} = \frac{20}{108} = \frac{5}{27}\)…