Hand written solution required

There are / children in a nursery and only one person in charge of taking care of them. Every once in a while a baby starts crying demanding the babysitter's attention. If the babysitter is busy with another baby, the new crying baby must wait their turn. If at time f a baby is calm, then the probability that they start crying and demand to be attended to in the time interval (t, t + h] is equal to Ah to(h).If at time t a baby is being cared for by the babysitter then the probability that they calm down in the time interval (t, t + h] is equal to uth to(h). Suppose that X, := number of babies that are demanding to be attended in time 6. We assume Xo = 0 What is the probability that there will ultimately be 0 babies waiting to be seen? (Hint: In this case we have a birth-death process with birth-death rates are, respectively, M = (N -i)> if0