A science class has 5 girls and 5 boys in the seventh grade and 9 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 girls?
Write your answer as a fraction in simplest form.
There are 10 students in the seventh grade and 10 in the eighth grade, for a total of 20 students. There are 5 girls in the seventh grade and 9 in the eighth grade, for a total of 14 girls.
The probability of selecting a girl from the seventh grade is 5/10 = 1/2.
The probability of selecting a girl from the eighth grade is 9/10.
To find the probability of both events happening (selecting a seventh-grade girl AND selecting an eighth-grade girl), multiply the probabilities:
(1/2) * (9/10) = 9/20
Therefore, the probability of selecting a seventh-grade girl and an eighth-grade girl is 9/20.