Solution:
Given that:
[tex]\begin{gathered} \text{Number of boys =2} \\ \text{Number of girls =10} \\ \text{Total population =12} \end{gathered}[/tex]Given that half of the girls wear glasses, this implies that
[tex]\text{Number of girls with glasses = 5}[/tex]The probability of an event is expressed as
[tex]Pr(\text{event)}=\frac{\text{Number of desired outcome}}{Number\text{ of favourable outcome}}[/tex]Thus, the probability that a student selected at random is a girl with glasses is evaluated as
[tex]\begin{gathered} Pr(\text{girl with glasses})=\frac{\text{number of girls with glasses}}{total\text{ number of students}} \\ =\frac{5}{12} \end{gathered}[/tex]Hence, the probability that the student selected at random is a girl with glasses is
[tex]\frac{5}{12}[/tex]