Another common case where you get positive EV insurance is when the cost paid by you and the cost paid by the insurerer, when the bad event happens, are significantly different.
For example, if you get extended phone / device insurance from a manufacturer, when the device fails you would have to pay the retail price for a new device. The manufacturer however only needs to pay the production price, which given margins can be a small fraction of the retail price. Thus the manufacturer can set a premium that is (in expectation) somewhere in between those two prices, and you both benefit.
Another common case where you get positive EV insurance is when the cost paid by you and the cost paid by the insurerer, when the bad event happens, are significantly different.
For example, if you get extended phone / device insurance from a manufacturer, when the device fails you would have to pay the retail price for a new device. The manufacturer however only needs to pay the production price, which given margins can be a small fraction of the retail price. Thus the manufacturer can set a premium that is (in expectation) somewhere in between those two prices, and you both benefit.