Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then

Question

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is :

TestHub · Accepted Answer

A 7 R , 5 B ​ B 5 R , 7 B ​ C 6 R , 6 B ​ ​ P ( B ) = 3 1 ​ ⋅ 12 5 ​ + 3 1 ​ ⋅ 12 7 ​ + 3 1 ​ ⋅ 12 6 ​ required probability = 3 1 ​ ⋅ [ 12 5 ​ + 12 7 ​ + 12 6 ​ ] 3 1 ​ ⋅ 12 5 ​ ​ = 18 5 ​ ​

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