[T01]

You're right!

Yes, this reasoning is correct. Other than in exceptional circumstances, the expected value of an insurance policy is negative, so if minimizing expected financial losses is all that's important to you, you shouldn't buy insurance.

Does this mean that it is irrational to buy insurance? Not necessarily. Along with wishing to minimize their expected financial losses, people also frequently want to avoid disaster. If you travel without insurance, you run a small risk that a serious disease or accident could be financially catastrophic to you; if you buy insurance, you eliminate this disastrous possibility at a small financial cost to yourself. In fact, given that your desire to avoid disaster is sufficiently strong, it may be that the expected utility of buying insurance is positive, even though the expected monetary value is negative. This shows how expected utility can differ from expected monetary value, even concerning financial matters.