For at least some kinds of insurance, there's an economy of scale involved that reduces overall cost and hassle for some kinds of event. At many doctors and hospitals, you really want the negotiated healthcare rates that insurance companies get rather than the list rates. It's very nice if you are involved in a car accident to have an insurance company deal with the other parties rather than you having to do so.
For some, this may even extend to small amounts - it may be convenient to have replacement protection for your phone rather than having to agonize over whether to repair or replace if you drop it.
Hey, everyone! So I've been reading an article about the expected utility, apparently to figure out whether the risk is worth taking you multiply expected value of the outcome by it's probability.
And apparently insurance companies can make money because the expected utility of buying insurance is lower than it's price.
So why would buying insurance be the rational action? I mean intuitively it makes sense(you want to avoid the risk), but it doesn't seem to fit well with this idea. If insurance is almost by definition is worth slightly less than it's price, how is it worth buying?
(sorry if it's a dumb question)