The computer lab at King Saud University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 20 students per hour, with the service rate being described by an exponential distribution. Calculate the following operating characteristics of the service system.

1. Probability of no students in the system.
2. The probability of having 2 students in the system.
3. The probability of having more than 4 students in the system.
4. The probability of having less than 4 students arrive at time 0.5 hr.
5. Probability of no student arrive at time 0.5 hr.