Government approval for a nuclear power plant on the California coast requires a hazard evaluation. Included is a probability analysis of various potentially damaging accidents or natural disasters.
Compute the probability of at least one occurrence, (1) in a single year and (2) sometime in the next 100 years, from each of the following potentially damaging events, all of which arise from independent Poisson processes:
(a) impact from an airplane crash, presumed to occur in the vicinity of the generator site at a mean annual rate of .000001.
(b) being hit by a large tsunami (tidal wave), known to occur once every 1,000 years with a further chance of 1/500 of hitting a particular location the width of the generator site.
(c) an earthquake causing rupture in the reactor cooling system. This could be only from a Richter-8 or greater shock whose epicenter falls near the generator site. This event is judged to have a mean rate of .00001 per year.