1. A professor holds regular office hours to assist students with their academic inquiries. The office hours are between 2:00-3:30 pm on Tuesdays and Thursdays. On average,12 students visit the professor every week (she is only available during her office hours). The professor can provide effective assistance tofive students per hour. Suppose you are tasked with analyzing this system as an M/M/1 model. Respond to the following questions:
   1. Calculate the probability of no patient in the queue.
   2. Calculate the probability of two patients waiting in the queue.
   3. What is the average number of patients in the system?