Earthquakes occur in a given region in accordance with a Poisson process with rate 5 per year.
(a) What is the probability there will be at least two earthquakes in the first half of 2015?
(b) Assuming that the event in part (a) occurs, what is the probability that there will be no earthquakes during the first 9 months of 2016?
(c) Assuming that the event in part (a) occurs, what is the probability that there will be at least four earthquakes over the first 9 months of the year 2015?