A science class has 3 girls and 3 boys in the seventh grade and 3 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 boys?

Write your answer as a fraction in simplest form.

To find the probability that both students selected are boys, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:
The teacher can select one student from the seventh grade, and then one student from the eighth grade. Since there are 3 girls and 3 boys in the seventh grade and 3 girls and 7 boys in the eighth grade, the total number of possible outcomes is 6 (2 students from the seventh grade multiplied by 10 students from the eighth grade).

Number of favorable outcomes:
To have both students be boys, the teacher needs to choose a boy from the seventh grade and a boy from the eighth grade. There are 3 boys to choose from in the seventh grade and 7 boys to choose from in the eighth grade. So the total number of favorable outcomes is 3 * 7 = 21.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 21 / 60
Probability = 7 / 20

Therefore, the probability that the students the teacher selects are both boys is 7/20.

for the 7th grade, the probability is 3 out of a total of 6 students. for 8th grade, there are 7 out of a total of 10 students. 3/6 times 7/10 is 7/20.