Question

A math class has 5 girls and 5 boys in the seventh grade and 5 girls and 7 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both girls? Write your answer as a fraction in simplest form.

Answer 1

Answer:

$\dfrac{5}{24}$

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

$\dfrac{5}{10}=\dfrac{1}{2}$

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

$\dfrac{5}{12}$

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

$\dfrac{1}{2}\cdot \dfrac{5}{12}=\dfrac{5}{24}$