Question

The probability that a patient arriving at an emergency unit needs to stay overnight is estimated to be 0.2. Assume the patients are admitted for overnight stay independent of each other. (a) The doctor has seen 5 patients in the first hour. What is the probability that more than 4 have to stay overnight? (b) A doctor starts her shift at 8PM. What is the probability that the first patient that will be registered for an overnight stay is the 4-th patient? (c) The emergency unit has a capacity of 5 beds. Each shift starts with all the beds free (patients are being transferred to a hospital by the end of the shift). Calculate the expected number of patients the doctor needs to see till all 5 beds are occupied.