Answer:
[tex]\dfrac{5}{24}[/tex]
Step-by-step explanation:
A math class has 5 girls and 5 boys in the seventh grade, 10 students in total. The probability of choosing one girl from this class is
[tex]\dfrac{5}{10}=\dfrac{1}{2}[/tex]
A math class has 5 girls and 7 boys in the eighth grade, 12 students in total. The probability of choosing one girl from this class is
[tex]\dfrac{5}{12}[/tex]
The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. The probability that the students she selects are both girls is
[tex]\dfrac{1}{2}\cdot \dfrac{5}{12}=\dfrac{5}{24}[/tex]