Two types of vehicle use the university central bus station: Uni-links and National Express coaches.

a) On average, a National Express coach arrives every two hours. What is the probability that only one bus will arrive in a four hour period?

b) On the U1 Uni-link bus route, buses either go to the airport or to the docks. Other Uni-link routes do not go to the airport. At the bus station, half of the U1 buses which arrive are going to the airport. At midday, 10% of the Uni-link buses are full. Of these particular buses, 30% are airport buses on the U1 route. U1 buses make up 40% of the Uni-link arrivals at the bus station. What is the probability that a bus is full at midday, given that it is an Airport U1 bus?

c) Are the events ‘bus is full' and ‘bus is going to the airport' independent? Show your reasoning.