However, with many forms of insurance the expected value is very nearly 1. Term life, for example, pays out 90%+ of premiums as death benefits. You are unlikely to get any of that money, as most policies do not pay out; but the low probability of a payout multiplied by a comparably high death benefit results in E(X) not to far from 1.
Another reason we keep paying for insurance even with bad expected values (e.g., title insurance) is because we have no choice about the matter. If I want a mortgage, I need title insurance, even though only a small fraction of the premiums are actually paid out as claims.
Another reason we keep paying for insurance even with bad expected values (e.g., title insurance) is because we have no choice about the matter. If I want a mortgage, I need title insurance, even though only a small fraction of the premiums are actually paid out as claims.