Customers arrive at a printing shop as a Poisson process with intensity = 3 customers per hour.

(a) What is the probability that no customers arrive during the morning hours 8 am to 12 noon?

(b) Given that the shop opens at 8 am, what is the probability that exactly two customers have arrived by 10 am and a total of five have arrived by 12 noon?

(c) What is the distribution of the time at which the first afternoon customer arrives?