USC is the strategy consulting firm which divides the consultants into 3 classes: Associates, Managers, and Partners. Firm has been stable in size for last twenty years. There has been - and are anticipated to be- 200 Associates, 50 Managers, and 20 Partners in steady state.
The work environment at firm is very competitive. After 5 years of working as Associate, consultant goes "either up or out"; that is, becomes the Manager, or is dismissed from company. Number of Associates dismissed from company, without being promoted to Manager, is traditionally about thirty per year.
Similarly, after many more years, a Manager either becomes the Partner, or is dismissed from company. As the policy, firm recruits new Iowa USC graduates as Associates; no hires are made at Manager or Partner level. If manager is promoted to Partner she/he remains as the Partner for 10 years on average, and then leaves company.
i) On average, how many new MBAs HKA needs to hire every year to maintain same number of Associates, Managers, and Partners?
ii) Find probability that Associate will be promoted to Manager?
iii) If the Associate is promoted to Manager, how many years she/he serves as Manager?