(a)
Poisson processes model events that occur randomly when you know the mean number of events within any given interval and all disjoint intervals (of any size) are independent.
Since meteors arrive independently of each other, a Poisson process is reasonable.
(b)
Compute probability:
We have
(c)
Let Window A be the first hour, Window B be the second through fourth hours, and Window C be the complete four hours.
The background rate is
Now the desired probability is:
The last line follows because