Question

In a certain clinic, visitors are diagnosed independently from one another. The probability that a visitor stays overnight is 0.2. i) The clinician has diagnosed 5 visitors in the first hour, what is the probability that more than 4 visitors will stay overnight. ii) A clinician's shift starts at 8:00 pm, what is the probability that the first visitor that will be registered for an overnight stay is the 4-th visitor? iii) The clinic has a capacity of 5 seats. Each shift starts with free seats. Calculate the expected number of visitors the clinician needs to see until all 5 seats are occupied.