Five students—the females Ann and Betty and the males Clint, Douglas, and Edward—are rated equally qualified for admission to law school, ahead of other applicants.

However, all but two positions have been filled for the entering class. The admissions committee can admit only two more students, so it decides to randomly select two of these five candidates. For this strategy, let y =

number of females admitted. Using the first letter of the name to denote a student, the different combinations that could be admitted are (A, B), (A, C), (A, D), (A, E), (B, C), (B, D), (B, E), (C,D), (C, E), and (D, E).

(a) Construct the probability distribution for y.

(b) Construct the sampling distribution of the sample proportion of the students selected who are female.