$$\frac{1}{3}(\frac{5}{6}+\frac{1}{12}+\frac{1}{3})$$ $$=\frac{1}{3}(\frac{10}{12}+\frac{1}{12}+\frac{4}{12})$$ $$=\frac{1}{3}(\frac{15}{12})$$ $$=\frac{5}{12}$$