A math class has 5 girls and 5 boys in the seventh grade and 7 girls and 1 boy 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.
There are 10 students in the seventh grade and 8 students in the eighth grade, so there are a total of 10 x 8 = 80 different pairs of students that the teacher could choose.
Out of the 5 boys in the seventh grade, the teacher could choose any one of them, and out of the 1 boy in the eighth grade, the teacher must choose that one boy. Therefore, there are 5 x 1 = 5 different pairs of boys that the teacher could choose.
The probability of selecting a pair of boys is then:
5 / 80 = 1 / 16