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
- A \(\frac{25}{64}\)
- B \(\frac{25}{64}\)
- C \(\frac{27}{64}\)
- D \(\frac{35}{54}\)
Answer & Solution
Correct Answer
(A) \(\frac{25}{64}\)
Step-by-step Solution
Detailed explanation
\(P(\text{1R from P, 2B from Q}) = \frac{4}{9} \times \frac{\binom{6}{2}}{\binom{9}{2}}\) \(P(\text{1R from P, 2B from Q}) = \frac{4}{9} \times \frac{15}{36} = \frac{4}{9} \times \frac{5}{12} = \frac{20}{108} = \frac{5}{27}\)…
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