Cars, camping trailers, and motorcycles arrive at the Maybury State Park toll booth acoording to independent Poisson processes. The toll booth opens at 6:00am. Cars arrive about once every five minutes. camping trailers arrive about once every 30 minutes. Motocycies arrive about once every 10 minutes. (1) Find the probability that in the rst 20 minutes, exactly three vehicles, two cars and one camping trailer, arrive at the toll booth. (2) Find the probability that the seventh car arrives within 45 minutes. {3} At the toll booth, the chance that a driver has exact change is 1/4, independent of vehicle. Find the probability that no vehicle has exact change in the rst 10 minutes. (4) What is the expected time between arrivals of vehicles at the toll booth? (5) What is the probability that the interarrival time between first vehicle and second vehicle exceeds 5 minutes