Insurance Runs on Expected Value

Every insurance premium is calculated with expected value. An insurer estimates the chance of a claim and its average cost, multiplies them to get the expected loss per policy, then charges a bit more to cover overhead and profit.

From your side, the premium has a slightly negative expected value — on average you pay in more than you get back. Paying it is still rational, because a single uninsured disaster could wipe you out. That is why EV alone does not settle every choice: utility, the personal value of money, matters too.