Trucks at a single platform weigh-bridge arrive according to Poisson probability distribution. The time required to weigh the truck follows an exponential probability distribution.

The mean arrival rate is 12 trucks per day, and the mean service rate is 18 trucks per day. Determine the following:

1. What is the probability that no trucks are in the system?

2. What is the average number of trucks waiting for service?

3. What is the probability that an arriving truck will have to wait for service?