first try
you get defective/nondefective/defective
(2/10) (8/9) (1/8) = 1/45
second try
nondefective/defective/defective
(8/10) (2/9) (1/8) = 1/45
probability = 1/45 + 1/45 = 2/45
there couldn't be defective/defective/nondefective because according to you, it must be exactly 3 trials, so why would you want to try again after you get 2 defectives.
however.. if you want to consider defective/defective/nondefective
then it should be
2/45 + (2/10) (1/9) (8/8) = 1/15
Hope this helps.