Question

A bag contains 10 balls out of which \( k \) are red and \( (10-k) \) are black, where \( 0 \le k \le 10 \). 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. \( \dfrac{7}{11} \)
• B. \( \dfrac{7}{55} \)
• C. \( \dfrac{14}{55} \)
• D. \( \dfrac{7}{110} \)

Hint:

In Bayes’ theorem problems, always identify prior probabilities clearly before computing conditional probabilities.

Answer 1

The Correct Option is B