To calculate the probability of selecting two boys, we first need to determine the total number of possible outcomes for selecting one student from each grade.
We have 3 boys in the seventh grade and 1 boy in the eighth grade. So the total number of possible outcomes is 3 * 1 = 3.
Next, we need to determine the number of favorable outcomes, which is the event of selecting two boys.
We have 3 boys in the seventh grade, so the probability of selecting a boy from the seventh grade is 3/6. Similarly, we have 1 boy in the eighth grade, so the probability of selecting a boy from the eighth grade is 1/5.
To find the probability of both events happening, we multiply the two probabilities:
P(Selecting a boy from seventh grade) = 3/6
P(Selecting a boy from eighth grade) = 1/5
P(Selecting both boys) = P(Selecting a boy from seventh grade) * P(Selecting a boy from eighth grade)
P(Selecting both boys) = (3/6) * (1/5)
P(Selecting both boys) = 3/30
P(Selecting both boys) = 1/10
Therefore, the probability that the teacher selects two boys is 1/10.