A company has three different facilities A, B and C. Facilities A and B are used for production and can be modeled as two independent Poisson processes with rate lambdaA and lambdaB orders/day, respectively. Facility C is a customer service department which processes the items returned by the costumers. Let assume that the probability of product A and B being returned are ra and rb, respectively.

a) What is the probability that in a fixed amount of time (T days), facility B receives twice (or more) orders than facility A.

b) Assume that facilities A and B can ship the orders on the same day that they were received. What is the probability that in T days, Facility C receive twice (or more) returned product of A comparing to B.