CUMULATIVE RISK FOR RANDOM EVENTS

 

Suppose that a random event occurs, on the average, once every 100 years.  The risk (or probability) that this event will occur in any 10-year period is:

              Risk   =   1 - [1 - 1/(R.I.)]n    
                        =   1- [1 - 1/(100)]10  
                        =   1 - [0.99]10     =   0.096 (or 9.6%)

 

Similarly, we can calculate the cumulative risks for various other time periods (for R.I. = 100):

TIME  PERIOD (n) [1 - 1 / (R.I.)]n CUMULATIVE RISK
20 years 0.82 18%
25 years 0.78 22%
69 years 0.50 50%
100 years 0.37 63%