A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of ? = 5 vehicles per day (approximately Poisson in nature)

The mechanic crew can service an average of ? = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.
a. What is the probability that the system is empty?
b. What is the probability that there is precisely one vehicle in the system?
c. What is the probability that there is more than one vehicle in the system?
d. What is the probability of 5 or more vehicles in the system?

(a)P0 = 1 - 5/10 = 0.50; (b) Pn > 1 = (5/10 )2 = 0.25; the probability of exactly one is 1 - .50 - .25 = .25;
(c) 0.25 as previously calculated; (d) the probability of five or more is Pn > 4 = (5/10 )5 = 0.0313.