A nurse specializes in caring for patients diagnosed with the disease described in Exercise 38.20.
a. The nurse cares for one patient at a time since the care is given in the patient's home, and constant monitoring of the patient is needed. She begins caring for that patient as soon as the diagnosis is given, and she cares for the patient until death. Then she is reassigned to a new patient. What is the expected time until her 3rd patient dies?
b. The nurse wakes up and realizes that her patient's "call" button is lit. Unfortunately she doesn't know how long it has been lit. She knows that it wasn't lit 10 minutes ago, when she fell asleep. So it could have been pressed at anytime during the previous 10 minutes, and she is worried that her patient has been waiting too long. What is the probability that the patient pressed the call button in the first 30 seconds that the nurse was asleep?
c. Given that the call button was not pressed in the first 30 seconds, what is the probability it was pressed during the last 2 minutes?