There are possible scenarios :

A) White ball is replaced from A into B and white ball is picked up : (1 / 3) * (5 / 12) = 5 / 36

B) White ball is replaced from A into B and black ball is picked up : (1 / 3) * (7 / 12) = 7 / 36

C) Black ball is replaced from A into B and white ball is picked up : (2 / 3) * (4 / 12) = 8 / 36

D) Black ball is replaced from A into B and black ball is picked up : (2 / 3) * (8 / 12) = 16 / 36

So P(ball picked will be white one) : = [ A) + C) ] / [ A) + B) + C) + D) ]

= (5 + 8) / (5 + 7 + 8 + 16)

= 13 / 36

Hence the correct answer is 13 / 36