If we look at it purely in terms of numbers, you have:

p = probability that something will go wrong (e.g. 1/1000)

Lm = monetary loss if not insured (e.g. $10000)

Li = intangible loss if not insured

**that the insurance would prevent**, both short term and long term (let's assume none here)

C = cost of insurance (e.g. $20)

For these numbers, the cost of insurance is too expensive, because the breakeven cost would be:

(Lm + Li) * p = $10000 * 1/1000 = $10

so it is better to not get it.

The problem is in the Li term. For something like life insurance, it is pretty high (you cannot work for the rest of your life -> how do you put a number on that? I guess you sum up all the lost income and future medical bills. But, for something like emergency travel insurance, I think it's pretty low (they only pay the hospital bill and that's it), assuming you can afford the hospital bill.

What do you guys think? Is my analysis right?

I also suspect that because insurance companies always have to make a profit, the answer to this question is very likely to be "no, don't get insurance" all the time. In fact, mathematically, it's the same as playing the lottery.