2/3 (not 1/2)
You know that you do not have Bag B ( two black marbles) so there are three possibilities
You chose Bag A , first white marble. The other marble will be white
You chose Bag A , second white marble. The other marble will be white
You chose Bag C , the white marble. The other marble will be black
So 2 out of 3 possibilities are white.
Why not 1/2? You are selecting marbles, not bags.
You know that you do not have Bag B ( two black marbles) so there are three possibilities
You chose Bag A , first white marble. The other marble will be white
You chose Bag A , second white marble. The other marble will be white
You chose Bag C , the white marble. The other marble will be black
So 2 out of 3 possibilities are white.
Why not 1/2? You are selecting marbles, not bags.