Passengers arrive at a train station according to a Poisson process with rate and wait for

Passengers arrive at a train station according to a Poisson process with rate

λ and wait for a train to arrive. Independently, trains arrive at the same station according to a Poisson process with rate μ. Suppose that each time a train arrives, all the passengers waiting at the station will board the train. The train then immediately leaves the station. If there are no passengers waiting at the station, the train will not wait until passengers arrive. Suppose that at time 0, there is no passenger waiting for a train at the station. For t > 0, find the probability that at time t also there is no passenger waiting for a train.