A math class has girls and boys in the seventh grade and girls and 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

How many of each gender are in the classes?

If you have 1/2cup of water and you take out 3/8 of water how much do you have left

Madison:

1/2
for you to be specific we need to
know each gender # for each grade
AL:
1 4 4
-X-=-
2 4 8

4 3 1
- - - =-
8 8 8

To find the probability of selecting two girls, we need to determine the total number of possible outcomes and the number of favorable outcomes.

First, let's find the total number of possible outcomes. The teacher can select any student from the entire class for the first slot, and then any student from the entire class (including both seventh and eighth graders) for the second slot. Since there are ( girls + boys) students in the seventh grade and ( girls + boys) students in the eighth grade, the total number of possible outcomes is ( girls + boys) × ( girls + boys).

Next, let's find the number of favorable outcomes. The teacher can only choose a girl from the seventh grade, and then only choose a girl from the eighth grade. So the number of favorable outcomes is girls × girls.

Now we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes.

Probability = ( girls × girls) / (( girls + boys) × ( girls + boys)).

Therefore, the probability of selecting two girls is:
Probability = ( girls × girls) / (( girls + boys) × ( girls + boys)).

Please substitute the given values (number of girls and boys in each grade) into the formula and simplify the expression to obtain the probability as a fraction in simplest form.