1. (2020 Exam) Subway trains arrive at a station at a Poisson rate of 20 per hour. 25% of the trains are express and 75% are local. The types of each train are independent. An express takes 16 minutes to get to work and a local takes 28 minutes to get to work. You always take the first train to arrive. Your co-worker always takes the first express. You both are waiting at the same station. (a) Find the mean time between the arrivals of new trains. (b) Find the probability that the first train enters is an express train. (c) Find the probability that, in the first 15 mins, only one local train arrives. (d) Suppose that 20 trains have arrived in one hour. Find the probability that only 4 trains are express. (e) Find your expected arrival time to work. (f) Find your co-worker expected arrival time to work