A science class has 3 girls and 7 boys in the seventh grade and 2 girls and 2 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?
7/10 * 2/4 = ____
I am sure that oobleck meant to say
(3/10)(2/4)
To find the probability that the students the teacher selects are both girls, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. Since the teacher is selecting one student from the seventh grade and one student from the eighth grade, we need to multiply the number of students in each grade. There are 3 girls and 7 boys in the seventh grade, which gives us 3 + 7 = 10 students. Similarly, there are 2 girls and 2 boys in the eighth grade, giving us 2 + 2 = 4 students. Therefore, the total number of possible outcomes is 10 * 4 = 40.
Now let's calculate the number of favorable outcomes, which is the number of ways to select two girls, one from the seventh grade and one from the eighth grade. We can choose one girl from the seventh grade in 3 ways and one girl from the eighth grade in 2 ways. Therefore, the number of favorable outcomes is 3 * 2 = 6.
Finally, to calculate the probability of selecting two girls, we divide the number of favorable outcomes by the total number of possible outcomes. Therefore, the probability is 6 / 40 = 0.15 or 15%.