What does the expected value for this problem mean, in layman's terms?

So there problem states:

Suppose that a school has 20 classes:

16 with 25 students in each

3 with 100 students in each

1 with 300 students, for a total of 1000 students.

a)

What is the average class size?

b)

Select a student randomly out of the 1000 students. Let the random variable X equal the size of the class to which this student belongs, and define the p.m.f. of X.

c)

Find E (X), the expected value of X.

So for a), the average class size is 50 because there's 1000 students/20 classes, or it can be viewed as a weighted average: [16(25)+3(100)+1(300)]/1000. So this makes sense to me because if you were to take a student at random, they would belong to a class of 50 students on average.

For b), if X is the size of the class to which a student belongs, then X = is the set of random variables, which are the class sizes: {25, 100, 300}. So the p.m.f. is the probability of someone being in a class of 25, 100, and 300, respectively. There are 25*16 = 400, 100*3 = 300, and 300*1 = 300 students in each of the class sizes, so out of 1000 students, the respective probabilities are 0.4, 0.3, and 0.3, when x (the class size ) = 25, 100, and 300, respectively.

So f(x) = {0.4, 0.3, 0.3} for x = {25,100,300}

Thus, for c) the expected value E[X] = x1(f(x1))+...x3(f(x3)) = 25*0.4+100*0.3+300*0.3 = 130.

So this is saying that the expected outcome of choosing a student out of 1000 is that they belong to a class size of 130, right?

Clearly, 50 and 130 are not equivalent. So if 50 is the average class size, then wouldn't each student, on average, belong to a class of 50 students? Or is this saying that each class category, on average, has 130 students?

This is the part that isn't clear to me. Is there a very simple way of explaining this?