Chapter 9.3, Problem 65E

Medicine. After bypass surgery, patients are placed in an intensive care unit (ICU) until their condition stabilizes. Then they are transferred to a cardiac care ward (CCW), where they remain until they are released from the hospital. In a particular metropolitan area, a study of hospital records produced the following data: each day $2\%$ of the patients in the ICU died, $52\%$ were transferred to the CCW, and the remainder stayed in the ICU. Furthermore, each day $4\%$ of the patients in the CCW developed complications and were returned to the ICU, $1\%$ died while in the CCW, $22\%$ were released from the hospital, and the remainder stayed in the CCW.

(A) In the long run, what percentage of the patients in the ICU are released from the hospital?

(B) In the long run, what percentage of the patients in the CCW die without ever being released from the hospital?

(C) What is the average number of days that a patient in the ICU will stay in the hospital?