Question

Building codes often tie the level of seismic hazard used in design to the ground shaking that on average will be reached or exceeded in 475 years. This is known as a Mean Recurrence Interval (MRI).
Use the Binomial PDF as a model for solving this problem. Answers must be in decimal form rounded to three digits.

a) What is the probability that a seismic event with an MRI of 475 years will occur at least once in 475 years?   


b) What is the probability that a seismic event with an MRI of 475 years will NOT occur in the first 100 years of a structure's life?  

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 1/475

N = number of trials

R = desired success

A)

N = 475

P(at least 1) = 1 - p(0) = 1 - 475c0*((1/475)^0)*(1-(1/475))^475-0

= 0.63250814038

B)

N = 100

P = 1 - (1/475)

R = 100

P(100) = 0.81