Q1) Both undergraduates and postgraduates can use the university cafeteria. Each diner can choose between buying a meal or bringing a packed lunch. (Everyone has exactly one meal each, no more and no less). The cafeteria offers a daily choice between a hot meal or a cold meal. A survey of undergraduate diners finds that 40% of them bring their own food.
Overall, only 25% of the diners bring their own food. Postgraduates make up one fifth of the diners in the cafeteria.

a) What is the probability that a diner is an undergraduate and has bought a meal?

b) What is the probability that someone who has bought a meal is a postgraduate?

c) Give two different examples from the question of mutually exclusive events.

Q2) Two types of vehicle use the university central bus station: Uni-link buses 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) On average, a certain number, k, of National Express coaches go to Bournemouth every day. It is found that the probability of n coaches going to Bournemouth in a day is e ^-k What is n?