Possible cases of balls can be choosen from bag 1 =
P(WW) =(4/6)*(3/5)
P(WB)=(4/6)*(2/5)
P(BW)=(2/6)*(4/5)
P(BB)=(2/6)*(1/5)
So in case WW in bag 2 = 7W+4B
In case WB in bag 2= 6W+5B
In case BW in bag 2= 6W+5B
in case BB in bag 2 = 5W+6B
probability of choosing while ball from bag 2=
(4/3)*(3/5)*(7/11)+(4/6)*(2/5)*(6/11)+(2/6)*(1/5)*(5/11)+(2/6)*(4/5)*(6/11)= 19/33