California earthquakes: We most often hear of the power of earthquakes given in terms of the Richter scale, but this tells only the power of the earthquake at its epicenter. Of more immediate...

California earthquakes: We most often hear of the power of earthquakes given in terms of the Richter scale, but this tells only the power of the earthquake at its epicenter. Of more immediate importance is how an earthquake affects the location where we are. Seismologists measure this in terms of ground movement, and for technical reasons they find the acceleration of ground movement most useful. For the purpose of this problem, a major earthquake is one that produces a ground acceleration of at least 5% of g, where g is the acceleration4 due to gravity near the surface of the Earth. In California, the probability p(n) of one’s home being affected by exactly n major earthquakes over a 10-year period is given approximately5 by

a. What is the probability of a California home being affected by exactly 3 major earthquakes over a 10-year period?

b. What is the limiting value of p(n)? Explain in practical terms what this means.

c. What is the probability of a California home being affected by no major earthquakes over a 10- year period?

d. What is the probability of a California home being affected by at least one major earthquake over a 10-year period? Hint: It is a certainty that an event either will or will not occur, and the probability assigned to a certainty is 1. Expressed in a formula, this is Probability of an event occurring + Probability of an event not occurring = 1 . This, in conjunction with part c, may be helpful for part d.