Q156. A state corrections system has established a new drug treatment facility for first offenders. The center has a capacity of 1000.

Inmates may leave the facility in either of two ways. In any period, there is a 10 percent probability that an inmate will be judged rehabilitated, in which case s/he will be released at the beginning of the following period.. There is also a 5 percent chance that an inmate will escape during each period. Rehabilitated addicts have a 20 percent chance of relapsing in each period; escapees have a 10 percent chance of being recaptured each period. Both recidivists and recaptured escapees are returned to the facility and have priority over new offenders.

Questions

If it operates at full capacity, how many of the original inmates will be resident at the facility 10 periods later?
How many new offenders can be admitted during each of the next 2 periods?
What happens if we modify the model to allow for a small possibility of death or a change in the probability of relapse?