Of all the students in a certain dormitory,  ~$\frac{1}{2}$~ are first-year students and the rest are second-year students.  If  ~$\frac{4}{5}$~  of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?

~$\frac{1}{15}$~

~$\frac{1}{5}$~

~$\frac{4}{15}$~

~$\frac{1}{3}$~

~$\frac{2}{5}$~