Flower manufacturer has noticed that the number of faulty Flowers detected in a production depends on the supervisor on duty and is detected according to a Poisson Process. There are only 2 supervisors: A and B, in the firm. The average number of faulty Flowers is 3 per day when A is on duty, while the average number of faulty Flowers is 4 per day when B is on duty. quality of one day's production does not have an effect on the next day. B works 4 out of 5 days, while A works 3 out of 5 days.

a) What is the probability that no faulty Flowers will be produced tomorrow, if B is on duty?

b) What is the probability that no faulty Flowers will be produced in the next two days?

c) Suppose at least one faulty Flower was produced yesterday, what is the probability that A was on duty?