Use the method of your choice to determine the following probability. Selecting at random a green long-sleeved shirt from a closet in which five-sixths of the shirts are short-sleeved and one-sixth are long-sleeved and one-third of the long-sleeved shirts are green. (Type an integer or a simplified fraction.)

Step 1 ：The problem is asking for the probability of selecting a green long-sleeved shirt. We know that one-sixth of the shirts are long-sleeved and one-third of the long-sleeved shirts are green.

Step 2 ：We can calculate this probability by multiplying these two probabilities together.

Step 3 ：Let's denote the probability of a shirt being long-sleeved as \(P(L) = \frac{1}{6}\) and the probability of a long-sleeved shirt being green as \(P(G|L) = \frac{1}{3}\).

Step 4 ：The probability of selecting a green long-sleeved shirt is then given by \(P(G \cap L) = P(L) \times P(G|L)\).

Step 5 ：Substituting the given values, we get \(P(G \cap L) = \frac{1}{6} \times \frac{1}{3} = \frac{1}{18}\).

Step 6 ：Final Answer: The probability of selecting a green long-sleeved shirt from the closet is \(\boxed{\frac{1}{18}}\).