Imagine there is a disease that has a one in a million chances to kill you every year, unless you pay 1 million dollars.
An insurer comes around and says “hey, pay me 2 dollars a year, and if the disease happens to you, I’ll pay for the treatment”. Does this sound like a good service for you?
From the point of view of the insurer, if they insure a million persons they are going to get 2 million dollars each year, but only have to pay for one treatment. Does this sound like a profitable business for you?
Mathematically it might make sense to save up the money and just pay it if it happens. From an odds point of view you are overpaying the insurance. But what if you’re unlucky and it happens to you in the first year? Odds are small, but it could happen.
Basically insurance is a known cost, that defends you from an unknown one. On average, most people lose money, but for people more unlucky than the average, insurance minimises risk.
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