Answer:
The probability that both students are of the same type is .
Step-by-step explanation:
The students in 435 are: {3 sophomores, 8 juniors and 13 seniors}
Number of students in 435 = 3 + 8 + 13 = 24
The students in FYS are: {5 sophomores, 7 juniors and 6 seniors}.
Number of students in FYS = 5 + 7 + 6 = 18
The teacher picks 1 student from each class.
The probability that both students are of the same type is:
P (Same type students) = P (Both are Sophomores) + P (Both are Juniors)
+ P (Both are Seniors)
= P (Sophomore ∩ Course 435) × P (Sophomore ∩ Course FYS)
+ P (Junior ∩ Course 435) × P (Junior ∩ Course FYS)
+ P (Senior ∩ Course 435) × P (Senior ∩ Course FYS)
Thus, the probability that both students are of the same type is .