The Math Behind Insurance.

  I work in a place where most people have government issued medical insurance, no personal insurance, no car insurance.  I don't even think they have insurance on their houses.

So when I talk about insurance, my students do not relate to it.  I admit, the only reason I knew about insurance before I graduated from high school was thanks to a class I took as a senior.

In that class, they had a variety of people from car sales to home sales, and so many more but they did make sure an insurance agent came in to talk to us about house, car, and all other types they sold.

The first thing insurance companies rely on is the law of large numbers. An example of this is when flipping a coin. On the first flip there is a 50 percent chance of getting a heads.  On the second flip, the chance of getting two heads in a row is 1/2 * 1/2 or 1/4 = 25%.  For the third flip, getting three heads in a row is 1/2 * 1/2 * 1/2 is 1/8 or 12.5%.  As the number of flips increases the chance of getting heads all in a row decreases such as flipping 6 heads in a row is 1/64 or 1.5%.

If instead you check for the percent of heads versus tails you get, the more times you flip the coin, the closer the percent gets to 50%.   Insurance companies keep track of each event such as car crashes, tornadoes taking out houses, etc and the larger the sample the more accurate the mathematical probability.

The second concept they use is one of "weighted probability" which takes into account everything.  If you played a dice game with a man where you would get $6 for every 6 you roll but you'd have to pay him $2 for any other number,  is it worth playing? 

You know the chance of rolling a 6 is 1/6 while the chance of rolling any other number is 5/6.  To calculate the weighted probability, its (-2)(5/6) + (6)(1/6) = -.66 or you would lose 66 cents each game. 

The idea is that more people will have nothing happen than those who have something happen.  So if you were a small insurance company with 1000 clients.  Say 1 house catches fires each year so the probability is 1/1000 of that happening.  Therefore the chances of the house not catching fire is 999/1000.  The replacement cost of the house is $200,000.  As far as premiums, each person pays $20 per month for a total of $240 per year.

The mathematics would be -200,000(1/1000) + 240(999/1000) = -200 + 239.76 = a profit of $39.76 per person.  This means your company will make a profit of $39,760 based on 1000 x $39.76.

This is a simple example but it gives a better idea of how insurance companies work.  Hope you find this interesting.  Let me know what you think, I'd love to hear.