First, note the number of tiles in each color. So there are 6 black tiles and 9 white tiles.
The probability of picking a black tile the first time is 6/15 which is equal to
2/5
Now, with black tile gone there are 5 black tiles and 9 white tiles.
The probability of picking a black tile now is
5/14.
But because both picks have to happen, multiply the fractions resulting in
1/7