For a specific site, earthquakes above magnitude 7 have a return period of 500 years. We are designing a dam with a design life of 100 years. We want to design this dam with a 1% probability of damage during it's lifetime. Effects of each earthquake are statistically independent.

a)Assuming that you can model magnitude 7 earthquakes following a Bernoulli sequence, what is the probability of damage to the dam by a single earthquake?

b)What would be the probability of damage to the dam in the next 40 years? Use the results of part a and assume that this can be modeled as a Poisson process.