Iam waiting for two friends to arrive at my house. the time until a arrives is exponentially distributed with rate lambda(a) and the time until b arrives is exponentially distributed with rate lambda(b). once they arrive, both will spend exponentially distributed times, with respective rates u(a) and u(b) at my home before departing. the four exponential random variables are independent.

a) what is the probability that a arrives before and departs after b?

b) what is the expected time of the last departure?