Problem
A mid-management team consists of forty people, 25 males and 15 females. Recently top management selected three people from this team for promotion. It was stated that the selections were based on random selection. All three people selected were males. The females are upset and believe that there may have been more than random selection involved here.
a) What probability distribution should be used to analyze this situation and what is the probability that all three promotions would go to males if the selections were random?
b) What is the probability that all three promotions were of males? Show how you calculated that probability.
c) Do you believe that the females have a valid complaint in this situation and why or why not?