A science class has 3 girls and 3 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 girls?
independent events
... multiply the individual probabilities to find the probability of both
probability of 7th grade girl is ... 3 / (3 + 3)
probability of 8th grade girl is ... 7 / (7 + 1)
Prob(girl from 7th grade) = 3/6 = 1/2
prob(girl from 8th grade) = 7/8
prob(both girls) = (1/2)(7/8) = 7/16
To find the probability that the teacher selects two girls, we need to calculate the ratio of the number of favorable outcomes (two girls selected) to the total number of possible outcomes.
First, let's determine the total number of possible outcomes. The teacher can select one student from the seventh grade (3 girls + 3 boys = 6 options) and one student from the eighth grade (7 girls + 1 boy = 8 options). So, the total number of possible outcomes is 6 * 8 = 48.
Next, we need to determine the number of favorable outcomes, which is the number of combinations where two girls are selected. We can choose one girl from the seventh grade (3 options) and one girl from the eight grade (7 options), so the number of favorable outcomes is 3 * 7 = 21.
Therefore, the probability that the teacher selects two girls is 21/48 or simplified to 7/16.
Thus, the probability that the students she selects are both girls is 7/16.