JEE Mains · Maths · STD 11 - 14. probability
A bag contains 10 balls out of which k are red and \((10-k)\) are black, where \(0\le k\le10.\) If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:
- A \(\frac{7}{11}\)
- B \(\frac{7}{55}\)
- C \(\frac{7}{110}\)
- D \(\frac{14}{55}\)
Answer & Solution
Correct Answer
(D) \(\frac{14}{55}\)
Step-by-step Solution
Detailed explanation
Probability \(=\frac{{ }^1 C _0 \cdot{ }^9 C _3}{\sum_{ k =0}^{10}{ }^{ k } C _0 \cdot{ }^{10- k } C _3}\) \(=\frac{{}^{9}C_{3}}{{}^{10}C_{3}+{}^{9}C_{3}+{}^{8}C_{3}+...{}^{3}C_{3}}\) \(=\frac{{}^{9}C_{3}}{{}^{11}C_{4}}=\frac{14}{55}\)
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