Let's assume the number of students in the class be x.
Given that, Two-thirds of students in a class are girls.
So, number of girls [tex] =\frac{2}{3} x [/tex]
Now ne-half of the girls wear glasses. So, one-half of [tex] \frac{2}{3} x [/tex] is
= [tex] \frac{1}{2} *\frac{2}{3} x [/tex]
=[tex] \frac{1}{3} x [/tex] Cancel out 2 from both numerator and denominator.
So, one third of the students are girls who wear glasses.
So, the correct choice is E.