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Law of Large Numbers

​​​Insurance companies uses the “Law of Large Numbers” and probability to determine the chance of an event occurring.  If the chance of someone having a car accident is one in one hundred, then insurance companies collect premiums from 100 people to pay the claim that one driver will incur. This is called “spreading the risk”. It is important for insurance companies to adequately gauge the hazards (items that increase the chance of loss) of a risk before insuring it.  If they don’t research and know a business or the habits of an individual and they guess wrong in predicting the chance of something happen the insurance company could lose money.  If they do this often enough then the company suffers. 


• Start with 100 individuals driving a Honda Accord each costing $25,000.

• Assume that if involved in an accident your vehicle is a total loss.

• Assume the chance of being in an accident is one out of 100 people.

• Total loss   _______ / # insureds_______ = premium per insured

No Peeking- Here's the Answer!
25,000 / 100 = $250 insurance premium


The Law of Large Numbers means the larger the number of risks (e.g. cars or homes etc.) that an insurance company insures the closer they will be able to predict the actual results of the chance of an accident occurring. Of course it is still up to chance but past experience is a good indicator of the future. 


Which of the following statements agrees with Law of Large Numbers? (psst… there is more than one true statement)

A. If you look at too small a number of risk, you will not be able to make an accurate prediction of losses within that group.

B. If you have enough units to study, you can tell exactly who will have a loss.

C. If you have enough units to study, you will be able to tell approximately how many units will have losses.

D. The smaller the number of risks studied, the less accurate your loss predictions will be. 

No Peeking- Here's the Answer!
A,C, and D are correct.  B is not correct as you cannot tell exactly.

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