Reduction of risk:

Risk Pooling:

Risk pooling is mechanism to defray risk. Its operation depends on the Law of Large Numbers.

Law  of  large numbers: In  repeated  independent trials with probability  p  of success in each trial, the chance that the percentage of success differs from the probability  p by more them a fixed positive amount  e ≥ 0 converges to zero as number of trials  n  goes to infinity for every positive  e .  If you recall from the probability theory covered  in MEC-003,  the  toss of a fair coin n times will yield an expected value of  1/2  for getting a head as n -> ∞  .  Along with it, the variance  (see Appendix at the end) will tend  to decline. Therefore, while we cannot predict the number of heads when a coin is tossed once, we can do so with, say,  10,000 tosses. Thus,  the  lesson  is,  by pooling  many  independent risks, insurance companies can treat uncertain outcomes as almost certain.