Question

It can be argued that it is not worth designing protection against a 100 year hurricane as such an event is not likely in one's lifetime. Based on the worldwide average life expectancy at birth is 71.0 years (2012 data), what is the probability of one 100 year event in a lifetime of an average human being? What is the probability of two 100 year events in a 71 year lifetime? What is the probability of one or two 100 year events in a 71 year lifetime?

Answer 1

Here as we know here that the event is occuring once in 100 year.

so as the distribution of an event occuring is poisson where x is the number of events occuring in 71 year lifetime.

Here,

expected number of 100 year events occuring in a 71 year lifetime = 71/100 = 0.71

so here poisson parameter = = 0.71

probability distribution

f(x) = e^-0.71 0.71^x/x! ; x = 0,1,2,3..

so first question

what is the probability of one 100 year event in a lifetime of an average human being?

Pr(x = 1) = e^-0.71 0.71¹/1! = 0.3491

Q.2What is the probability of two 100 year events in a 71 year lifetime?

P(X = 2) = e^-0.71 0.71²/2! = 0.1239

Q.3 What is the probability of one or two 100 year events in a 71 year lifetime?

P(X = 1 or 2) = P(X = 1) + P(X = 2) = 0.3491 + 0.1239 = 0.4730