Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selecte

Question

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is n m ​ , where gcd ( m , n ) = 1 , then m + n is equal to :

TestHub · Accepted Answer

Bag contains 4 white and 6 black balls A : first ball selected is black B : Second ball is also black ​ P ( B A ​ ) = 10 4 ​ × 9 6 ​ + 10 6 ​ × 9 5 ​ 10 6 ​ × 9 5 ​ ​ = 24 + 30 30 ​ = 54 30 ​ = 9 5 ​ m + n = 5 + 9 = 14 ​

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