Question: There high schools have senior classes of size 100, 400, and 500, respectively. Here are two schemes for selecting a student from among the three senior classes:
A: Make a list of all 1000 seniors, and choose a student at random from this list
B: Pick on school at random, then pick a student at random from the senior class in that school.
Show that these two schemes are not Probabilistically equivalent. Here is a third scheme.
C: Pick school i with probability pi (p1 + p2 + p3 = 1), then pick a student at random form the senior class in that school.
Find the probabilities p1, p2, and p3 which make scheme C equivalent to scheme a.