The average number of trucks passing by a house between 8am and 4pm (8 hours) in 1 day is 4 (Poisson process).

1. During the course of 7 days, what is the probability that 2 trucks appear on one of the days, 3 trucks appear on four of the days, and 5 trucks appear on two of the days?
2. During those 7 days, what is the expected number of days 2 or 3 trucks will drive by?
3. Given that during 7 days there were 3 days with 5 trucks, find the probability that each of the other 4 days had 2 trucks drive by.
4. On the first day there was at least one truck that drove by. Find the probability that it drove by before 12:00PM.