If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red

Question

A box B₁ contains 1 white ball, 3 red balls and 2 black balls. Another box B₂ contains 2 white balls, 3 red balls and 4 black balls. A third box B₃ contains 3 white balls, 4 red balls and 5 black balls.

If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B₂ is 

(A) 116/181 

(B) 126/181

(C) 65/181 

(D) 55/181

Answer 1

Correct option is (D) 55/181

Let A : one ball is white and other is red 

E₁ : both balls are from box B₁ 

E₂ : both balls are from box B₂ 

E₃ : both balls are from box B₃