ANSWER
P(both girls) = 3/20
EXPLANATION
The probability of the event E where the teacher selects one student from each grade and both are girls is:
[tex]P(E)=P(girl\text{ 7th)}\cdot P(girl\text{ 8th)}[/tex]The probability of selecting a girl from 7th grade is:
[tex]P(\text{girl 7th)}=\frac{\text{ \# of girls in 7th grade}}{\text{ \# of students in 7th grade}}=\frac{5}{10}=\frac{1}{2}[/tex]The probability of selecting a girl from 8th grade is:
[tex]P(\text{girl 8th)}=\frac{\text{ \# of girls in8th grade}}{\text{ \# of students in 8th grade}}=\frac{3}{10}[/tex]The probability of event E is then:
[tex]P(E)=\frac{1}{2}\cdot\frac{3}{10}=\frac{3}{20}[/tex]