Actually, insurance is very often positive expected value for the individual. He's paying the insurance company $n, which the company reinvests for even higher expected value, which is how the company makes a profit even when it's paying out to its customers slightly more than they put in. It's essentially the bank model.

I suppose that even when insurance is negative, its primary function is to buy protection against being shunted to $0 value. You're paying value to eliminate risk.