Yes. The question is, GIVEN that a bunny has been drawn, what is the probability that it came from the green hat. This is an application of Bayes Theorem.If my reasoning flawed?
Consider the entire sample space to be of items drawn. He'll either draw from Hat Black or Hat Green. The probability that he draws from Hat Black is 30/36 (or the compliment of the probability that he draws from hat green, which you already calculated). The probability that he draws from Hat Green is 6/36. Now, OF the items in Hat Black 2/5 of them are bunnies. OF the items in Hat Green, 3/8 of them are bunnies. Therefore the probability that he draws a bunny GIVEN that he is drawing from Hat Black is (2/5)(30/36), and the probability that he draws a bunny GIVEN that he is drawing from Hat Green is (3/8)(6/36).
What YOU have to figure out, is GIVEN that he has drawn a bunny (we are reversing our "given" statements), what is the probability that he drew it from Hat Green? So what you have to do is consider the new sample space. In this case the "sample space" will be "drawing a bunny" (remember, that the GIVEN part of these problems defines the new sample space you are working from).