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

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

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

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