$0.096$ should be the correct answer, i.e. option $(a)$
Suppose that the side of larger cube is $10\;m$ then volume of the larger cube will be $10\times 10\times 10 = 1000\;m^{3}.$
After dividing the cube into $1000$ equal sized small cubes, volume of each smaller cube will be
$\left(\dfrac{10\times 10\times 10}{1000}\right) m^{3} = 1\,m^{3}.$
So the sides of the each of the smaller cube will be $1\;m,$ which is $10$ times less than the side length of larger cube.
So, each EDGE of the larger larger cube will contain $10$ smaller cube edges.
Each FACE of the larger cube will contain $10\times 10 = 100$ smaller cube faces.
Each CORNER of the larger cube will contain $1$ smaller cube corner.
Position of each of the smaller cube can be as follows:
$(A)$ It can be in the corners of the larger cube, In this case it would have three of its faces colored.
There are total
$8\text{(number of corners)}\times 1\text{(number of smaller cubes per corner)} = 8 \text{ such cubes}.$
$(B)$ It can be in the edges of the larger cube, In this case it would have two of its faces colored.
There are total
$12\text{(number of edges)}\times 8\text{(number of smaller cubes per edge excluding corner cubes of the edge)} = 96.$
$(C)$ It can be on the face of the larger cube but not in the edges of a face, in this case it would have one face colored.
There are total
$6\text{(number of faces)}\times 64\text{(number of smaller cubes per face excluding the edge & corner cubes)} = 384.$
$(D)$ It can be inside the core of the larger cube, in this case it will be uncolored.
There will be $512=( 1000 - (384 + 96 + 8))$ cubes.
Now since there are $96$ cubes out of $1000$ which have $2$ colored faces, so required probability =$\dfrac{96}{1000} = 0.096$
Now, since total number of edges in the larger cube $= 12,$
So, total number of smaller cubes with two colored faces $= 12\times 8 = 96.$