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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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:
Solution
Probability $ = \frac{{^1C_0} \cdot {^9C_3}}{\sum_{k=0}^{10} {^kC_0} \cdot {^{10-k}C_3}} $
$ = \frac{{^9C_3}}{{^0C_3} + {^1C_3} + {^2C_3} + \ldots + {^9C_3}} $
$ = \frac{{^9C_3}}{{^{11}C_4}} = \frac{14}{55} $
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