In seismology, an earthquake is said to be “strong” if it has a magnitude of at least six measured on the Richter scale. Imagine that in an area which is frequently hit by earthquakes, the number of strong earthquakes follows a Poisson process with a rate of 2.5 per year.

(i) What is the probability that there will be at least three earthquakes of that magnitude

(a) in a three-month period;

(b) in a year?

(ii) Find the probability that in the next 10 years there will be exactly 3 years in each of which there will be at least 3 strong earthquakes.