In reply to Bruce Hooker:
> Obviously the insurance companies like the scare stories, you know it makes sense, but if you want to calculate the risk just divide the possible payout + a bit of profit by the premium, not that high. Then ask yourself if you are feeling lucky
Of course, but when you do some risk management, you usually consider 2 main scenarios:
1/ what will most probably happen?
2/ what will probably not happen, but would have very high impact if it did?
And you plan for both.
From a statistical point of view, your mathematical expectation is already negative if you don't take an insurance - taking an insurance only makes it marginally worse, but you are improving your standard deviation a lot.
Another way to think of it: would you play the lottery every week? If so, don't take an insurance (you like surprises! but they rarely happen). If not, take one.