A science class has 3 girls and 7 boys in the seventh grade and 5 girls and 5 boysin 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?

To find the probability that the teacher selects two 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. The teacher can choose one student from the 7 boys in the seventh grade, which gives us 7 choices. Similarly, for the eighth grade, the teacher can choose one student from the 5 boys, giving us another 5 choices. The total number of possible outcomes is then 7 * 5 = 35.

Now, let's calculate the number of favorable outcomes, i.e., the number of ways the teacher can select two girls. From the seventh grade, the teacher can choose one girl from the 3 girls, which gives us 3 choices. From the eighth grade, the teacher can choose one girl from the 5 girls, giving us another 5 choices. The number of favorable outcomes is then 3 * 5 = 15.

Finally, 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
= 15 / 35
= 3 / 7
= 0.42857142857142855 (rounded to six decimal places)

Therefore, the probability that the teacher selects two girls is approximately 0.4286.

To find the probability that the teacher selects two girls, we need to determine the probability of selecting a girl from each grade and then multiply those probabilities together.

In the seventh grade, there are 3 girls and 10 students in total. Therefore, the probability of selecting a girl from the seventh grade is:

P(seventh grade girl) = Number of seventh grade girls / Total number of students in seventh grade
P(seventh grade girl) = 3 / 10

In the eighth grade, there are 5 girls and 10 students in total. Hence, the probability of selecting a girl from the eighth grade is:

P(eighth grade girl) = Number of eighth grade girls / Total number of students in eighth grade
P(eighth grade girl) = 5 / 10

Now, to find the probability that the teacher selects two girls, we multiply the probabilities together:

P(selecting two girls) = P(seventh grade girl) * P(eighth grade girl)
P(selecting two girls) = (3 / 10) * (5 / 10)
P(selecting two girls) = 15 / 100
P(selecting two girls) = 0.15

Therefore, the probability that the students she selects are both girls is 0.15 or 15%.

As Steve already did this for you, I don't know why you are repeating it.

... Anyway, prob(of your event)
= (3/10)(5/10)
= 15/100
= 3/20 , which is what Steve had told you.