Refer to Exercise 8.87 but now suppose the sampling is done in two stages: First a list is selected at random and then, from that list, two persons are selected at random without replacement.

Let Y denote the number of females in the sample.

(a) List the elementary outcomes concerning the possible selections of this and the possible compositions of the sample (use a tree diagram). Find their probabilities.

(Hint: Use conditional probability and the multiplication rule.)

(b) Determine the probability distribution of Y.