going to select the same two schools, number two and number four here.

And then within each school,

I'm going to select ten students by simple random sampling as stated here.

So I've got ten selected here and ten selected there.

So I'm picking 10 out of the 30 that are in school 2,

and 10 out of 100 that are in school 4.

So the conditional selection probability in school 2 is 10 over 30 or

one-third, and the conditional selection probability

of a student in school 4 is 10 over 100 or 0.1, as shown here.

Now, when I take the overall student selection probability,

I'm going to get 0.3 times a third is 0.1 in school 2,

and 1 times 0.1 is 0.1 in school 4.

I invert those, and sure enough, you see,

I get exactly the same base weight in these two cases.

That's not an accident, so we can just sketch out the calculation here.

If I look at school 2, let's do that one.

I've got a selection probability of 2

times and the proportion of its size of school 2.

So that's 30 out of, you see I've got the grand total here of 200 in the universe.

So 2 times 30 over 300, and then within the scale,

I'm going to pick 10, add up the 30 that are there.