cant find my mistake anywhere

each of the 3 identical boxes has 2 drawers. the first box, one a gold watch in each drawer. the 2nd box, has a silver watch in each drawer and the 3rd box has a gold watch in one drawer and a silver in the other. what is the probability of finding a gold watch in one drawer of a box given that the other drawer has a silver watch?

my working:

P ( gold l silver) = P ( gold and silver ) / P (silver)

= (1/3) / ( 1/3 + 1/6)

= 2/3

but the answer was 1/3

may i know what went wrong?

should i use bayes rule to solve this, how do i go about doing it?

thanks!